Let $R$ be a commutative ring with non-zero unity. If $\mathfrak{a}$ and $\mathfrak{b}$ are two fractional ideals of $R$ with $\mathfrak{a} \subseteq \mathfrak{b}$ , and if $\mathfrak{b}$ is invertible, then there is a fractional ideal $\mathfrak{c}$ of $R$ such that $\mathfrak{a} = \mathfrak{bc}$ , (one can choose $\mathfrak{c} = \mathfrak{b}^{-1}\mathfrak{a}$ .

Definition. Let $R$ be a commutative ring with non-zero unity and let $\mathfrak{a}$ and $\mathfrak{b}$ be ideals of $R$ The ring $R$ is a multiplication ring if $\mathfrak{a} \subseteq \mathfrak{b}$ , always implies that there exists a fractional ideal $\mathfrak{c}$ of $R$ such that $\mathfrak{a} = \mathfrak{bc}$

Bibliography

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M. LARSEN & P. MCCARTHY: Multiplicative theory of ideals. Academic Press. New York (1971).