Conditions of multiplicity and applications for almost Gorenstein graded rings

Koji Matsushita; Sora Miyashita

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arXiv · 2311.17387

Conditions of multiplicity and applications for almost Gorenstein graded rings

Koji Matsushita·Sora Miyashita

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Abstract

In this paper, we prove that if Cohen-Macaulay local/graded rings $R_1$, $R_2$ and $R$ satisfy certain conditions regarding multiplicity and Cohen-Macaulay type, then almost Gorenstein property of $R$ implies Gorenstein properties for all of $R_1$, $R_2$ and $R$. We apply our theorem to tensor products of semi-standard graded rings and some classes of affine semigroup rings, i.e., numerical semigroup rings, edge rings and stable set rings.

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Koji Matsushita, Sora Miyashita. 2023-11-29. Conditions of multiplicity and applications for almost Gorenstein graded rings. https://arxiv.org/abs/2311.17387

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