Remarks on almost Gorenstein rings

This paper investigates the relation between the almost Gorenstein properties for graded rings and for local rings. Once $R$ is an almost Gorenstein graded ring, the localization $R_M$ of $R$ at the graded maximal ideal $M$ is almost Gorenstein as a local ring. The converse does not hold true in gen...

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Bibliographic Details
Main Authors Endo, Naoki, Matsuoka, Naoyuki
Format Journal Article
LanguageEnglish
Published 25.07.2023
Subjects
Mathematics - Commutative Algebra
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Summary:This paper investigates the relation between the almost Gorenstein properties for graded rings and for local rings. Once $R$ is an almost Gorenstein graded ring, the localization $R_M$ of $R$ at the graded maximal ideal $M$ is almost Gorenstein as a local ring. The converse does not hold true in general. However, it does for one-dimensional graded domains with mild conditions, which we clarify in the present paper. We explore the defining ideals of almost Gorenstein numerical semigroup rings as well.
DOI:10.48550/arxiv.2307.13479