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.

Department(s)

Mathematics

Document Type

Article

DOI

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

Publication Date

2008

Journal Title

Proceedings of the American Mathematical Society

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