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=39723
Kernel congruence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Kernel_congruence&oldid=39723
This article was adapted from an original article by D.M. Smirnov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article