ideals in a Dedekind domain EveryIdealInADedekindDomainIsAFactorOfAPrincipalIdeal 2002-07-03 09:20:28 2008-04-29 17:40:07 Theorem Dedekind domain \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} 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.