Difference between revisions of "Kernel"
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Revision as of 12:13, 27 May 2008
In general, a kernel is a measure of the failure of a homomorphism to be injective.
In set theory, if 
and 
are sets, with 
a function mapping into , the kernel of is quotient set of under the equivalence relation 
defined as "
".
In group theory, if 
and 
are groups, and 
is a homomorphism of groups, the kernel of is the set of elements of that map to the identity of , i.e., the set 
. The kernel is a normal subgroup of , and in fact, every normal subgroup of is the kernel of a homomorphism.
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