OpenMath

OpenMath is an extensible standard for representing the semantics of mathematical objects.

https://openmath.github.io

OpenMath Signatures

Type System: sts2
Content Dictionary: algebraic_cats
CD Signature File: algebraic_cats.sts 

               
    Date:2002-07-06
    Author: Bill Naylor

monoid 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS name="mapsto" cd="sts"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMV name="Set"/>
        <OMS name="monoid" cd="generic_alg_cats"/>
      </OMA>
    </OMOBJ>
( Set ( Set Set >> Set ) Set >> monoid )

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monoid_set 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="monoid" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( monoid >> Set )

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monoid_operation 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="monoid" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( monoid >> ( Set Set >> Set ) )

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monoid_identity 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="monoid" cd="generic_alg_cats"/>
        <OMV name="Set"/>
      </OMA>
    </OMOBJ>
( monoid >> Set )

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Abelian_monoid 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS name="mapsto" cd="sts"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMV name="Set"/>
        <OMS name="Abelian_monoid" cd="generic_alg_cats"/>
      </OMA>
    </OMOBJ>
( Set ( Set Set >> Set ) Set >> Abelian_monoid )

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Abelian_monoid_set 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="Abelian_monoid" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( Abelian_monoid >> Set )

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Abelian_monoid_operation 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="Abelian_monoid" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( Abelian_monoid >> ( Set Set >> Set ) )

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Abelian_monoid_identity 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="Abelian_monoid" cd="generic_alg_cats"/>
        <OMV name="Set"/>
      </OMA>
    </OMOBJ>
( Abelian_monoid >> Set )

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ordered_monoid 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS name="mapsto" cd="sts"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMV name="Set"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMS cd="setname2" name="Boolean"/>
        </OMA>
        <OMS name="ordered_monoid" cd="generic_alg_cats"/>
      </OMA>
    </OMOBJ>
( Set ( Set Set >> Set ) Set ( Set Set >> Boolean ) >> ordered_monoid )

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ordered_monoid_set 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_monoid" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ordered_monoid >> Set )

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ordered_monoid_operation 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_monoid" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ordered_monoid >> ( Set Set >> Set ) )

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ordered_monoid_identity 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_monoid" cd="generic_alg_cats"/>
        <OMV name="Set"/>
      </OMA>
    </OMOBJ>
( ordered_monoid >> Set )

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ordered_monoid_order 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_monoid" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMS cd="setname2" name="Boolean"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ordered_monoid >> ( Set Set >> Boolean ) )

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ordered_Abelian_monoid 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS name="mapsto" cd="sts"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMV name="Set"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMS cd="setname2" name="Boolean"/>
        </OMA>
        <OMS name="ordered_Abelian_monoid" cd="generic_alg_cats"/>
      </OMA>
    </OMOBJ>
( Set ( Set Set >> Set ) Set ( Set Set >> Boolean ) >> ordered_Abelian_monoid )

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ordered_Abelian_monoid_set 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_Abelian_monoid" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ordered_Abelian_monoid >> Set )

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ordered_Abelian_monoid_operation 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_Abelian_monoid" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ordered_Abelian_monoid >> ( Set Set >> Set ) )

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ordered_Abelian_monoid_identity 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_Abelian_monoid" cd="generic_alg_cats"/>
        <OMV name="Set"/>
      </OMA>
    </OMOBJ>
( ordered_Abelian_monoid >> Set )

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ordered_Abelian_monoid_order 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/> <OMS name="ordered_Abelian_monoid" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMS cd="setname2" name="Boolean"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ordered_Abelian_monoid >> ( Set Set >> Boolean ) )

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groupoid 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS name="mapsto" cd="sts"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMS name="groupoid" cd="generic_alg_cats"/>
      </OMA>
    </OMOBJ>
( Set ( Set Set >> Set ) >> groupoid )

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groupoid_set 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="groupoid" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( groupoid >> Set )

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groupoid_operation 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="groupoid" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( groupoid >> ( Set Set >> Set ) )

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semigroup 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS name="mapsto" cd="sts"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMS name="semigroup" cd="generic_alg_cats"/>
      </OMA>
    </OMOBJ>
( Set ( Set Set >> Set ) >> semigroup )

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semigroup_set 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="semigroup" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( semigroup >> Set )

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semigroup_operation 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="semigroup" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( semigroup >> ( Set Set >> Set ) )

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Abelian_semigroup 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS name="mapsto" cd="sts"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMS name="Abelian_semigroup" cd="generic_alg_cats"/>
      </OMA>
    </OMOBJ>
( Set ( Set Set >> Set ) >> Abelian_semigroup )

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Abelian_semigroup_set 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="Abelian_semigroup" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( Abelian_semigroup >> Set )

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Abelian_semigroup_operation 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="Abelian_semigroup" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( Abelian_semigroup >> ( Set Set >> Set ) )

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group 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS name="mapsto" cd="sts"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMV name="Set"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMS name="group" cd="generic_alg_cats"/>
      </OMA>
    </OMOBJ>
( Set ( Set Set >> Set ) Set ( Set >> Set ) >> group )

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group_set 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="group" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( group >> Set )

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group_operation 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="group" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( group >> ( Set Set >> Set ) )

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group_identity 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="group" cd="generic_alg_cats"/>
        <OMV name="Set"/>
      </OMA>
    </OMOBJ>
( group >> Set )

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group_inverse 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="group" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( group >> ( Set >> Set ) )

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ordered_group 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS name="mapsto" cd="sts"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMV name="Set"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMS cd="setname2" name="Boolean"/>
        </OMA>
        <OMS name="ordered_group" cd="generic_alg_cats"/>
      </OMA>
    </OMOBJ>
( Set ( Set Set >> Set ) Set ( Set >> Set ) ( Set Set >> Boolean ) >> ordered_group )

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ordered_group_set 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_group" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ordered_group >> Set )

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ordered_group_operation 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_group" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ordered_group >> ( Set Set >> Set ) )

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ordered_group_identity 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_group" cd="generic_alg_cats"/>
        <OMV name="Set"/>
      </OMA>
    </OMOBJ>
( ordered_group >> Set )

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ordered_group_inverse 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/> <OMS name="ordered_group" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ordered_group >> ( Set >> Set ) )

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ordered_group_order 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_group" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMS cd="setname2" name="Boolean"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ordered_group >> ( Set Set >> Boolean ) )

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Abelian_group 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS name="mapsto" cd="sts"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMV name="Set"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMS name="Abelian_group" cd="generic_alg_cats"/>
      </OMA>
    </OMOBJ>
( Set ( Set Set >> Set ) Set ( Set >> Set ) >> Abelian_group )

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Abelian_group_set 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="Abelian_group" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( Abelian_group >> Set )

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Abelian_group_operation 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="Abelian_group" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( Abelian_group >> ( Set Set >> Set ) )

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Abelian_group_identity 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="Abelian_group" cd="generic_alg_cats"/>
        <OMV name="Set"/>
      </OMA>
    </OMOBJ>
( Abelian_group >> Set )

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Abelian_group_inverse 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="Abelian_group" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( Abelian_group >> ( Set >> Set ) )

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ordered_Abelian_group 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS name="mapsto" cd="sts"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMV name="Set"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMS cd="setname2" name="Boolean"/>
        </OMA>
        <OMS name="ordered_Abelian_group" cd="generic_alg_cats"/>
      </OMA>
    </OMOBJ>
( Set ( Set Set >> Set ) Set ( Set >> Set ) ( Set Set >> Boolean ) >> ordered_Abelian_group )

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ordered_Abelian_group_set 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_Abelian_group" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ordered_Abelian_group >> Set )

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ordered_Abelian_group_operation 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_Abelian_group" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ordered_Abelian_group >> ( Set Set >> Set ) )

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ordered_Abelian_group_identity 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_Abelian_group" cd="generic_alg_cats"/>
        <OMV name="Set"/>
      </OMA>
    </OMOBJ>
( ordered_Abelian_group >> Set )

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ordered_Abelian_group_inverse 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_Abelian_group" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ordered_Abelian_group >> ( Set >> Set ) )

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ordered_Abelian_group_order 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_Abelian_group" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMS cd="setname2" name="Boolean"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ordered_Abelian_group >> ( Set Set >> Boolean ) )

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ringoid 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS name="mapsto" cd="sts"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMS name="ringoid" cd="generic_alg_cats"/>
      </OMA>
    </OMOBJ>
( Set ( Set Set >> Set ) ( Set Set >> Set ) >> ringoid )

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ringoid_set 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ringoid" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ringoid >> Set )

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ringoid_times 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ringoid" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ringoid >> ( Set Set >> Set ) )

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ringoid_plus 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ringoid" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ringoid >> ( Set Set >> Set ) )

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ring 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS name="mapsto" cd="sts"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMV name="Set"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMS name="ring" cd="generic_alg_cats"/>
      </OMA>
    </OMOBJ>
( Set ( Set Set >> Set ) ( Set Set >> Set ) Set ( Set >> Set ) >> ring )

Content Dictionary Entry.

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ring_set 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ring" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ring >> Set )

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ring_times 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ring" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ring >> ( Set Set >> Set ) )

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ring_plus 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ring" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ring >> ( Set Set >> Set ) )

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ring_zero 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ring" cd="generic_alg_cats"/>
        <OMV name="Set"/>
      </OMA>
    </OMOBJ>
( ring >> Set )

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ring_negative 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ring" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ring >> ( Set >> Set ) )

Content Dictionary Entry.

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ordered_ring 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS name="mapsto" cd="sts"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMV name="Set"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMS cd="setname2" name="Boolean"/>
        </OMA>
        <OMS name="ordered_ring" cd="generic_alg_cats"/>
      </OMA>
    </OMOBJ>
( Set ( Set Set >> Set ) ( Set Set >> Set ) Set ( Set >> Set ) ( Set Set >> Boolean ) >> ordered_ring )

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ordered_ring_set 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_ring" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ordered_ring >> Set )

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ordered_ring_times 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_ring" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ordered_ring >> ( Set Set >> Set ) )

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ordered_ring_plus 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_ring" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ordered_ring >> ( Set Set >> Set ) )

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ordered_ring_zero 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_ring" cd="generic_alg_cats"/>
        <OMV name="Set"/>
      </OMA>
    </OMOBJ>
( ordered_ring >> Set )

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ordered_ring_negative 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_ring" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ordered_ring >> ( Set >> Set ) )

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ordered_ring_order 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="ordered_ring" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMS cd="setname2" name="Boolean"/>
        </OMA>
      </OMA>
    </OMOBJ>
( ordered_ring >> ( Set Set >> Boolean ) )

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non_commutative_ring 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS name="mapsto" cd="sts"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMV name="Set"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMS name="non_commutative_ring" cd="generic_alg_cats"/>
      </OMA>
    </OMOBJ>
( Set ( Set Set >> Set ) ( Set Set >> Set ) Set ( Set >> Set ) >> non_commutative_ring )

Content Dictionary Entry.

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non_commutative_ring_set 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="non_commutative_ring" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( non_commutative_ring >> Set )

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non_commutative_ring_times 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="non_commutative_ring" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( non_commutative_ring >> ( Set Set >> Set ) )

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non_commutative_ring_plus 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="non_commutative_ring" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( non_commutative_ring >> ( Set Set >> Set ) )

Content Dictionary Entry.

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non_commutative_ring_zero 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="non_commutative_ring" cd="generic_alg_cats"/>
        <OMV name="Set"/>
      </OMA>
    </OMOBJ>
( non_commutative_ring >> Set )

Content Dictionary Entry.

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non_commutative_ring_negative 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="non_commutative_ring" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( non_commutative_ring >> ( Set >> Set ) )

Content Dictionary Entry.

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Euclidean_domain 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS name="mapsto" cd="sts"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMV name="Set"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMS name="Euclidean_domain" cd="generic_alg_cats"/>
      </OMA>
    </OMOBJ>
( Set ( Set Set >> Set ) ( Set Set >> Set ) Set ( Set >> Set ) ( Set >> Set ) >> Euclidean_domain )

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Euclidean_domain_set 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="Euclidean_domain" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( Euclidean_domain >> Set )

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Euclidean_domain_times 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="Euclidean_domain" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( Euclidean_domain >> ( Set Set >> Set ) )

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Euclidean_domain_plus 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="Euclidean_domain" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( Euclidean_domain >> ( Set Set >> Set ) )

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Euclidean_domain_zero 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="Euclidean_domain" cd="generic_alg_cats"/>
        <OMV name="Set"/>
      </OMA>
    </OMOBJ>
( Euclidean_domain >> Set )

Content Dictionary Entry.

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Euclidean_domain_negative 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="Euclidean_domain" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( Euclidean_domain >> ( Set >> Set ) )

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Euclidean_domain_abs 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="Euclidean_domain" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( Euclidean_domain >> ( Set >> Set ) )

Content Dictionary Entry.

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field 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS name="mapsto" cd="sts"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMV name="Set"/>
        <OMV name="Set"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMS name="field" cd="generic_alg_cats"/>
      </OMA>
    </OMOBJ>
( Set ( Set Set >> Set ) ( Set Set >> Set ) Set Set ( Set >> Set ) ( Set >> Set ) >> field )

Content Dictionary Entry.

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field_set 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="field" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( field >> Set )

Content Dictionary Entry.

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field_times 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="field" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( field >> ( Set Set >> Set ) )

Content Dictionary Entry.

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field_plus 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="field" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( field >> ( Set Set >> Set ) )

Content Dictionary Entry.

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field_one 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="field" cd="generic_alg_cats"/>
        <OMV name="Set"/>
      </OMA>
    </OMOBJ>
( field >> Set )

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field_zero 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="field" cd="generic_alg_cats"/>
        <OMV name="Set"/>
      </OMA>
    </OMOBJ>
( field >> Set )

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field_reciprocal 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="field" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( field >> ( Set >> Set ) )

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field_negative 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="field" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( field >> ( Set >> Set ) )

Content Dictionary Entry.

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integral_domain 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS name="mapsto" cd="sts"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMV name="Set"/>
        <OMV name="Set"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
        <OMS name="integral_domain" cd="generic_alg_cats"/>
      </OMA>
    </OMOBJ>
( Set ( Set Set >> Set ) ( Set Set >> Set ) Set Set ( Set >> Set ) >> integral_domain )

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integral_domain_set 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="integral_domain" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="structure" cd="sts"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( integral_domain >> Set )

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integral_domain_times 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="integral_domain" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( integral_domain >> ( Set Set >> Set ) )

Content Dictionary Entry.

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integral_domain_plus 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="integral_domain" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( integral_domain >> ( Set Set >> Set ) )

Content Dictionary Entry.

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integral_domain_one 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="integral_domain" cd="generic_alg_cats"/>
        <OMV name="Set"/>
      </OMA>
    </OMOBJ>
( integral_domain >> Set )

Content Dictionary Entry.

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integral_domain_zero 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="integral_domain" cd="generic_alg_cats"/>
        <OMV name="Set"/>
      </OMA>
    </OMOBJ>
( integral_domain >> Set )

Content Dictionary Entry.

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integral_domain_negative 

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="sts" name="mapsto"/>
        <OMS name="integral_domain" cd="generic_alg_cats"/>
        <OMA>
          <OMS name="mapsto" cd="sts"/>
          <OMV name="Set"/>
          <OMV name="Set"/>
        </OMA>
      </OMA>
    </OMOBJ>
( integral_domain >> ( Set >> Set ) )

Content Dictionary Entry.

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