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
- [math]\displaystyle{ M \oplus F = G . \, }[/math]
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
- ↑ Lam, T. Y. (1978). Serre's Conjecture. p. 23. https://books.google.com/books?id=f-t6CwAAQBAJ&pg=PA23&dq=%22If+P+is+stably+free%2C+but+not+finitely+generated%2C+then+P+is+actually+free.%22.
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