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Stably free module

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

See also

References

^ Lang, Serge (1993), Algebra (Third ed.), Reading, Mass.: Addison-Wesley, ISBN 978-0-201-55540-0, Zbl 0848.13001
^ Lam, T. Y. (1978). Serre's Conjecture. p. 23.

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