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", 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 modules. Injective modules were introduced in and are discussed in some detail in the textbook .