If $R$ is a ring and $f\colon M\rightarrow N$ is a homomorphism of $R$ -modules, then a right inverse of $f$ is a homomorphism $g\colon N\rightarrow M$ such that $f\circ g$ is the identity map on $N$ . For a right inverse to exist, it is clear that $f$ must be an epimorphism. If a right inverse exists for every such epimorphism and all modules $M$ , then $N$ is said to be a projective module.

For fractional ideals over an integral domain $R$ , the property of being projective as an $R$ -module is equivalent to being an invertible ideal.

In particular, every fractional ideal over a Dedekind domain is invertible, and is therefore projective.