ideals in a Dedekind domain

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.

Title ideals in a Dedekind domain IdealsInADedekindDomain 2013-03-22 12:49:50 2013-03-22 12:49:50 yark (2760) yark (2760) 9 yark (2760) Theorem msc 11R37 msc 11R04 DivisorAsFactorOfPrincipalDivisor FundamentalTheoremOfIdealTheory