projective module
A module that is a direct summand of a free module; used in homological algebra and module theory.
A module that is a direct summand of a free module is called a projective module.
A free module has a basis; every free module is projective, but not conversely.
An injective module is the dual notion: every module can be embedded into an injective module.
From 射影 (projection) + 加群 (module). The term reflects the property that projective modules are direct summands of free modules, analogous to projection maps in linear algebra.