Stably free module

In mathematics, a stably free module is a module which is close to being free.

Definition

A module M over a ring R is stably free if there exists a free finitely generated module F over R such that $M\oplus F$ is a free module.

Properties

• A projective module is stably free if and only if it possesses a finite free resolution.
• An infinitely generated module is stably free if and only if it is free.

See also

• Free object
• Eilenberg–Mazur swindle
• Hermite ring

References

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