Remarks on almost Gorenstein rings

Fuente: arXiv
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Main Authors: Endo, Naoki, Matsuoka, Naoyuki
Format: Preprint
Published: 2023
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author Endo, Naoki
Matsuoka, Naoyuki
author_facet Endo, Naoki
Matsuoka, Naoyuki
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2307_13479
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Remarks on almost Gorenstein rings
Endo, Naoki
Matsuoka, Naoyuki
Commutative Algebra
13H10, 13A15, 13A02
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.
title Remarks on almost Gorenstein rings
topic Commutative Algebra
13H10, 13A15, 13A02
url https://arxiv.org/abs/2307.13479