An injective module is a type of module that has the property that any homomorphism from a submodule into it can be extended to a homomorphism from the entire module. This concept is closely related to various properties of rings and modules, particularly in the context of depth, regular sequences, and Cohen-Macaulay rings, as it influences their structure and classification. Injective modules play a significant role in understanding projective resolutions and the overall homological dimensions of algebraic structures.
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