split exact sequence - Wolfram|Alpha

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Input interpretation

split exact sequence

Definition

A short exact sequence of groups
0⟶A⟶B⟶C⟶0
is called split if it essentially presents B as the direct sum of the groups A and C.
More precisely, one can construct a commutative diagram as diagrammed above, where i is the injection of the first summand A and p is the projection onto the second summand C, and the vertical maps are isomorphisms.

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Related terms

commutative diagram | direct sum | short exact sequence

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