Stably free module explained

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

M ⊕ F is a free module.

Properties

• A projective module is stably free if and only if it possesses a finite free resolution.
• An infinitely generated module is stably free if and only if it is free.^[1]

See also

• Free object
• Eilenberg–Mazur swindle
• Hermite ring

Notes and References

1. Book: Lam, T. Y. . [{{Google books|plainurl=y|id=f-t6CwAAQBAJ|page=23|text=If P is stably free, but not finitely generated, then P is actually free.}} Serre's Conjecture]. 1978. 23.