Gorenstein rings and irreducible parameter ideals

Details Gorenstein rings and irreducible parameter ideals Gorenstein rings and irreducible parameter ideals

2006-08-26

arxiv.org/abs/math/0608661v2

Mathematics

Commutative Algebra

9 pages; submitted; Replacement: Coauthor H. Sakurai added, reference to work of J. R. Strooker added, introduction shortened

Scientific paper

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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