Category:Definitions/Projective Modules

This category contains definitions related to Projective Modules.
Related results can be found in Category:Projective Modules.

Let $A$ be a ring with unity.

Let $M$ be an $A$-module.

$M$ is projective if and only if there exists an $A$-module $N$ such that the direct sum $M \oplus N$ is a free module.