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.[1]
  • An infinitely generated module is stably free if and only if it is free.[2]

See also

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.
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