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
Free object
Eilenberg–Mazur swindle
Hermite ring
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.
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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