Stably free module

This article defines a property of a module over a commutative unital ring

Definition

Symbol-free definition

A module over a commutative unital ring is said to be stably free if there exists a free module with which its direct sum is again a free module.

Definition with symbols

A module $M$ over a commutative unital ring $R$ is said to be stably free if there exists a free $R$-module $F$ such that $M\oplus F$ is again free.

Relation with other properties

Stronger properties

• Free module

Weaker properties

• Projective module
• Flat module