Let $R$ be a Dedekind domain, and let $\mathfrak{a}$ and $\mathfrak{b}$ be ideals of $R$ Then there is an element $\omega$ and an ideal $\mathfrak{c}$ of $R$ such that $$\mathfrak{ac} = (\omega)$$ and $$\mathfrak{b+c} = R.$$

This result was proved by Steinitz in 1911.