Conditions of multiplicity and applications for almost Gorenstein graded rings

Koji Matsushita; Sora Miyashita

paper

Conditions of multiplicity and applications for almost Gorenstein graded rings

arXiv:2311.17387

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.

14 pages, comments are welcome!