1. Definition

2. Properties

3. See also

4. References

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 (Theorem XXI.2.1 of Lang's Algebra).
• An infinitely generated module is stably free if and only if it is free.{{fact|date=May 2017}}

See also

• Free object
• Eilenberg–Mazur swindle
• Hermite ring

References

• Page 840 of {{Lang Algebra|edition=3}}

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