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