Kernel congruence

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