Stably free module

Updated on Nov 16, 2023

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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 ⊕ F = G .

A projective module is stably free if and only if it possesses a finite free resolution (Theorem XXI.2.1 of Lang's Algebra).

An infinitely generated module is stably free if and only if it is free.

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