OpenMath is an extensible standard for representing the semantics of mathematical objects.
OpenMath is an extensible standard for representing the semantics of mathematical objects.
A CD of functions for relating ring elements their images in quotient rings
Written by Arjeh M. Cohen 2004-07-07
This symbol is a binary function whose first argument is a ring R and whose second argument is an ideal I of R. When applied to R and I, its value is the natural quotient map from R to the quotient ring R/I.
| [Next: quotient_by_poly_map] [Last: automorphism_group] [Top] |
This symbol is a binary function whose first argument is a ring R, and whose second argument is a univariate polynomial f with coefficients from R. So, if the indeterminate is X, when applied to R and f, the function has value the natural quotient map from R[X] to the quotient ring R[X]/(f).
| [Next: homomorphism_by_generators] [Previous: quotient_map] [Top] |
This is a function with three arguments the first two of which must be monoids F and K. The third argument should be a set or a list L of ordered pairs (lists of length 2). Each pair [x,y] from L consists of an element x from F and an element y from K. when applied to F, K, and L, the symbol represents the monoid homomorphism from F to K that maps the first entry x of each pair [x,y] to the second entry y of the same pair.
| [Next: automorphism_group] [Previous: quotient_by_poly_map] [Top] |
This is a function with a single argument which must be a ring. It refers to the automorphism group of its argument.
| [First: quotient_map] [Previous: homomorphism_by_generators] [Top] |