injective module
A module over a ring such that every injective homomorphism from a submodule can be extended to the whole module. Used in homological algebra.
Injective modules are used to construct the injective envelope of any module.
This theorem guarantees that there are enough injective modules.
射影加群 (projective module) is the dual notion: every surjective homomorphism onto it splits. Injective modules are about extending maps from submodules, while projective modules are about lifting maps through quotients.
入射包絡 (injective envelope) is the minimal injective module containing a given module. 入射加群 is the general concept, while 入射包絡 is a specific construction.
From 入射 (にゅうしゃ, 'injection' or 'injective') + 加群 (かぐん, 'module'). The term is a direct translation of the English mathematical term 'injective module'.