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 ${\displaystyle M\oplus F}$ is a free module.

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

• Free object
• Eilenberg–Mazur swindle
• Hermite ring

References

This linear algebra-related article is a stub. You can help Wikipedia by expanding it.

• v
• t
• e