injective module

Module that makes certain exact sequences split

EntityQ2716519

Subclass of: module
, injective object

Overview

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In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties with the Z-module Q of all rational numbers. Specifically, if Q is a submodule of some other module, then it is already a direct summand of that module; also, given a submodule of a module Y, any module homomorphism from this submodule to Q can be extended to a homomorphism from all of Y to Q. This concept is dual to that of projective modules. Injective modules were introduced in and are discussed in some detail in the textbook.

Overview

All data

16 statements · 25% with external sources · numbers in brackets are citations

Studied by: module theory
homological algebra
Dual notion (category theory): projective module

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statements

25%

externally sourced

Source last edited September 6, 2026. AIDb refreshes this page daily.

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AIDb. (2026). injective module (Q2716519). Retrieved from https://aidb.si/e/injective-module-Q2716519