Stably free module

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


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


  • 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


  • 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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