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Stably free module

Summary

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

Definition

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A module M over a ring R is stably free if there exists a free finitely generated module F over R such that   is a free module.

Properties

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  • 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

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References

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  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.