Remarks on almost Gorenstein rings

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 ([7, Theorems 2.7, 2.8], [8, Example 8.8]). 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.

KEYWORDS:

• Almost Gorenstein graded ring
• almost Gorenstein local ring
• numerical semigroup

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 13H10
• 13A15
• 13A02

Additional information

Funding

The first author was partially supported by JSPS Grant-in-Aid for Young Scientists 20K14299 and JSPS Grant-in-Aid for Scientific Research (C) 23K03058.