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
Canonical name	IdealsInADedekindDomain
Date of creation	2013-03-22 12:49:50
Last modified on	2013-03-22 12:49:50
Owner	yark (2760)
Last modified by	yark (2760)
Numerical id	9
Author	yark (2760)
Entry type	Theorem
Classification	msc 11R37
Classification	msc 11R04
Related topic	DivisorAsFactorOfPrincipalDivisor
Related topic	FundamentalTheoremOfIdealTheory