Remarks on almost Gorenstein rings

2023/07/25 by Endo, Naoki, Matsuoka, Naoyuki
#13A02 #13A15 #13H10 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.13479

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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