Work

When do pseudo‐Gorenstein rings become Gorenstein?

Year: 2025

Type: article

Abstract: We discuss the relationship between the trace ideal of the canonical module and pseudo‐Gorensteinness. In particular, under certain mild assumptions, we show that every positively graded domain that is both pseudo‐Gorenstein and nearly Gorenstein is Gorenstein. As an application, we clarify the relationships among nearly Gorensteinness, almost Gorensteinness, and levelness — notions that generalize Gorensteinness — in the context of standard graded domains. Moreover, we give a method for constructing quasi‐Gorenstein rings by taking a Veronese subalgebra of certain Noetherian graded rings.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70186

Author: Sora Miyashita

Institution: The University of Osaka

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Science and Technology Agency

Award: G4713469407