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[[Category:Homological algebra]]
In [[mathematics]], an '''injective module''' is a [[module (mathematics)|module]] ''Q'' that shares certain desirable properties with the '''Z'''-module '''Q''' of all [[rational number]]s. 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'', then 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 module]]s.
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