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What (who) is injective - definition
Injective hull
NOTION IN ABSTRACT ALGEBRA
Module of finite rank; Injective envelope
In mathematics, particularly in algebra, the injective hull (or injective envelope) of a module is both the smallest injective module containing it and the largest essential extension of it. Injective hulls were first described in .
Injective module
MATHEMATICAL OBJECT IN ABSTRACT ALGEBRA
Injective test lemma; Injective dimension; Baer's criterion; Self-injective ring
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.
Injective tensor product
In mathematics, the injective tensor product of two topological vector spaces (TVSs) was introduced by Alexander Grothendieck and was used by him to define nuclear spaces. An injective tensor product is in general not necessarily complete, so its completion is called the .
