PlanetMath: split short exact sequence

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split short exact sequence

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In an abelian category, a short exact sequence $0 \to A \buildrel f \over \to B \buildrel g \over \to C \to 0$ is split if it satisfies the following equivalent conditions:

(a) there exists a homomorphism $h : C \to B$ such that ;

(b) there exists a homomorphism $j : B \to A$ such that ;

In this case, we say that and are backmaps or splitting backmaps.

"split short exact sequence" is owned by antizeus.

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Other names:

backmap, splitting backmap

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Cross-references: direct sum, isomorphic, homomorphism, equivalent, short exact sequence, abelian category
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This is version 4 of split short exact sequence, born on 2002-01-05, modified 2003-09-20.
Object id is 1356, canonical name is SplitShortExactSequence.
Accessed 6641 times total.

Classification:

16E05 (Associative rings and algebras :: Homological methods :: Syzygies, resolutions, complexes)

Pending Errata and Addenda

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