PlanetMath: first isomorphism theorem

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first isomorphism theorem

(Theorem)

If $f : G\to H$ is a homomorphism of groups (or rings, or modules), then it induces an isomorphism $G/\ker f \cong {\rm im} f$ .

"first isomorphism theorem" is owned by rspuzio. [ full author list (2) | owner history (1) ]

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Cross-references: isomorphism, induces, modules, rings, homomorphism of groups
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This is version 5 of first isomorphism theorem, born on 2001-12-21, modified 2005-05-03.
Object id is 1114, canonical name is FirstIsomorphismTheorem.
Accessed 8887 times total.

Classification:

AMS MSC:	20A05 (Group theory and generalizations :: Foundations :: Axiomatics and elementary properties)
	13A15 (Commutative rings and algebras :: General commutative ring theory :: Ideals; multiplicative ideal theory)

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