Stably free module

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

Contents

1 Definition
2 Properties
3 See also
4 References

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).

See also

Free object

References

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