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September 2020 Local rings with self-dual maximal ideal
Toshinori Kobayashi
Illinois J. Math. 64(3): 349-373 (September 2020). DOI: 10.1215/00192082-8622656

Abstract

Let R be a Cohen–Macaulay local ring possessing a canonical module. In this paper, we consider when the maximal ideal of R is self-dual—i.e., it is isomorphic to its canonical dual as an R -module. Local rings satisfying this condition are called Teter rings, studied by Teter, Huneke–Vraciu, Ananthnarayan–Avramov–Moore, and others. In the one-dimensional case, we show such rings are exactly the endomorphism rings of the maximal ideals of some Gorenstein local rings of dimension one. We also provide some connection between the self-duality of the maximal ideal and near Gorensteinness.

Citation

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Toshinori Kobayashi. "Local rings with self-dual maximal ideal." Illinois J. Math. 64 (3) 349 - 373, September 2020. https://doi.org/10.1215/00192082-8622656

Information

Received: 15 March 2019; Revised: 22 April 2020; Published: September 2020
First available in Project Euclid: 16 July 2020

zbMATH: 07235508
MathSciNet: MR4132596
Digital Object Identifier: 10.1215/00192082-8622656

Subjects:
Primary: 13C14
Secondary: 13E15, 13H10

Rights: Copyright © 2020 University of Illinois at Urbana-Champaign

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Vol.64 • No. 3 • September 2020
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