202507031507

Tags : Homology Theory

Split Exact Sequences

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Definition

A split exact sequence is a special case of Short Exact Sequences that is described by the following shape.

$$0⟶M_1⟶M_1\oplus M_2⟶M_2⟶0$$

More generally a short exact squence is said to split if its isomorphic to a split exact sequence in the sense that the follwoing diagram commutes:

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References

• Short Exact Sequences
• Left and Right Inverses of Ring Homomorphisms