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 ${\displaystyle M\oplus F}$ is a free module.

Properties

• A projective module is stably free if and only if it possesses a finite free resolution. ^[1]
• An infinitely generated module is stably free if and only if it is free. ^[2]

See also

• Free object
• Eilenberg–Mazur swindle
• Hermite ring

References

1. Lang, Serge (1993), Algebra (Third ed.), Reading, Mass.: Addison-Wesley, ISBN   978-0-201-55540-0, Zbl   0848.13001
2. Lam, T. Y. (1978). Serre's Conjecture. p. 23.