stably free module
In mathematics, a stably free module is a module which is close to being free.
Definition
A module M over a ring R is stably free if there exists a free finitely generated module F over R such that is a free module.
Properties
- A projective module is stably free if and only if it possesses a finite free resolution.{{Lang Algebra|edition=3}}
- An infinitely generated module is stably free if and only if it is free.{{cite book|author=Lam, T. Y. |title=Serre's Conjecture|year=1978|url={{Google books|plainurl=y|id=f-t6CwAAQBAJ|page=23|text=If P is stably free, but not finitely generated, then P is actually free.}}|page=23}}