nLab fractional ideal

Given a commutative domain $k$, a fractional ideal of $k$ in the quotient field $Q(k)$ is a $k$-submodule $M\subset Q(k)$ such that there exist an element $c\in k$ such that $c M\subset k$.

If $k$ is Noetherian domain, then $c M$ is finitely generated, and hence $M$ is also a finitely generated $k$-module.

Fractional ideals are of importance in algebraic number theory.