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

M\oplus F=G.\,

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.

See also

References

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

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