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arXiv · 2307.13479

Remarks on almost Gorenstein rings

Naoki Endo·Naoyuki Matsuoka
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Abstract

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.

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Naoki Endo, Naoyuki Matsuoka. 2023-07-25. Remarks on almost Gorenstein rings. https://arxiv.org/abs/2307.13479

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