congruence

Let $\Sigma$ be a fixed signature, and $\mathfrak{A}$ a structure for $\Sigma$ . A congruence $\sim$ on $\mathfrak{A}$ is an equivalence relation such that for every natural number $n$ and $n$ -ary function symbol $F$ of $\Sigma$ , if $a_{i}\sim a_{i}^{\prime}$ then $F^{\mathfrak{A}}(a_{1},\ldots a_{n})\sim F^{\mathfrak{A}}(a_{1}^{\prime},% \ldots a_{n}^{\prime}).$

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