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Gorenstein rings and irreducible parameter ideals

Thomas Marley·Mark W. Rogers·Hideto Sakurai
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Abstract

Given a Noetherian local ring (R,m) it is shown that there exists an integer l such that R is Gorenstein if and only if some system of parameters contained in m^l 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.

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Thomas Marley, Mark W. Rogers, Hideto Sakurai. 2006-09-06. Gorenstein rings and irreducible parameter ideals. https://arxiv.org/abs/math/0608661

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