射しゃ影えい加か群ぐん

Meanings

1

noun

projective module

mathematics

A module that is a direct summand of a free module; used in homological algebra and module theory.

自じ由ゆう加か群ぐんの直ちょく和わ因いん子しである加か群ぐんを射しゃ影えい加か群ぐんという。
A module that is a direct summand of a free module is called a projective module.

flock, group, crowd

Similar words

自じ由ゆう加か群ぐん
A free module has a basis; every free module is projective, but not conversely.
入にゅう射しゃ加か群ぐん
An injective module is the dual notion: every module can be embedded into an injective module.

Etymology

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.