congruence

Let $\mathrm{\Sigma }$ be a fixed signature, and $𝔄$ a structure for $\mathrm{\Sigma }$. A congruence $\sim$ on $𝔄$ is an equivalence relation such that for every natural number $n$ and $n$-ary function symbol $F$ of $\mathrm{\Sigma }$, if $a_i\sim a_i^{\prime }$ then $F^{𝔄}(a_1,\mathrm{\dots }{a}_n)\sim F^{𝔄}(a_1^{\prime },\mathrm{\dots }{a}_n^{\prime }).$

Title	congruence
Canonical name	Congruence12
Date of creation	2013-03-22 13:46:38
Last modified on	2013-03-22 13:46:38
Owner	almann (2526)
Last modified by	almann (2526)
Numerical id	9
Author	almann (2526)
Entry type	Definition
Classification	msc 03C05
Classification	msc 03C07
Related topic	CongruenceRelationOnAnAlgebraicSystem