# Kernel congruence

From Encyclopedia of Mathematics

*of a homomorphism of algebraic systems*

The congruence (cf. Congruence (in algebra)) on consisting of all pairs for which . For any congruence on an algebraic system there is a homomorphism of this system for which is the kernel congruence. If is the kernel congruence of a strong homomorphism of an algebraic system onto a system , then the canonical mapping , where , is an isomorphism of the quotient system onto .

For references see Homomorphism.

**How to Cite This Entry:**

Kernel congruence.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Kernel_congruence&oldid=11822

This article was adapted from an original article by D.M. Smirnov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article