# OpenMath Content Dictionary: ring5

Canonical URL:
http://www.openmath.org/cd/ring5.ocd
CD Base:
http://www.openmath.org/cd
CD File:
ring5.ocd
CD as XML Encoded OpenMath:
ring5.omcd
Defines:
automorphism_group, homomorphism_by_generators, quotient_by_poly_map, quotient_map
Date:
2004-07-07
Version:
1 (Revision 1)
Review Date:
2006-06-01
Status:
experimental

A CD of functions for relating ring elements their images in quotient rings

Written by Arjeh M. Cohen 2004-07-07


## quotient_map

Description:

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.

Signatures:
sts

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## quotient_by_poly_map

Description:

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).

Signatures:
sts

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## homomorphism_by_generators

Description:

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.

Signatures:
sts

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## automorphism_group

Description:

This is a function with a single argument which must be a ring. It refers to the automorphism group of its argument.

Signatures:
sts

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