Conditions of multiplicity and applications for almost Gorenstein graded rings
Abstract
In this paper, we prove that if Cohen-Macaulay local/graded rings R1, R2 and R satisfy certain conditions regarding multiplicity and Cohen-Macaulay type, then almost Gorenstein property of R implies Gorenstein properties for all of R1, R2 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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