# Stably free module

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

## Definition

A finitely generated module *M* over a ring *R* is *stably free* if there exist free finitely generated modules *F* and *G* over *R* such that

## Properties

- A projective module is stably free if and only if it possesses a finite free resolution (Theorem XXI.2.1 of Lang's
**Algebra**). - An infinitely generated module is stably free if and only if it is free.

## References

- Page 840 of Lang, Serge (1993),
*Algebra*(Third ed.), Reading, Mass.: Addison-Wesley, ISBN 978-0-201-55540-0, Zbl 0848.13001

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