# 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 Congruence12 2013-03-22 13:46:38 2013-03-22 13:46:38 almann (2526) almann (2526) 9 almann (2526) Definition msc 03C05 msc 03C07 CongruenceRelationOnAnAlgebraicSystem