## Articles by College of Natural and Applied Sciences Faculty

#### Title

Gorenstein rings and irreducible parameter ideals

#### Abstract

Given a Noetherian local ring $(R,m)$ it is shown that there exists an integer $\ell$ such that $R$ is Gorenstein if and only if some system of parameters contained in $m^{\ell}$ generates an irreducible ideal. We obtain as a corollary that $R$ is Gorenstein if and only if every power of the maximal ideal contains an irreducible parameter ideal.

Mathematics

Article

#### DOI

https://doi.org/10.1090/s0002-9939-07-08958-7

2008

#### Journal Title

Proceedings of the American Mathematical Society

COinS