Stably free module
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
Properties[]
- A projective module is stably free if and only if it possesses a finite free resolution.[1]
- An 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.
Categories:
- Module theory
- Free algebraic structures