Article · Wikipedia archive · Last revised Jun 13, 2026

Stably free module

In mathematics, a stably free module is a module which is close to being free.

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Jun 13, 2026

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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 $M\oplus F$ 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

See also

References

References

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