A note on quasi-Gorenstein rings

TL;DR

This paper provides criteria for identifying quasi-Gorenstein rings and explores conditions under which they are Gorenstein, including a generalization of a known theorem.

Contribution

It introduces new criteria for quasi-Gorenstein rings and extends a theorem of Evans and Griffith to broader cases.

Findings

Criteria for quasi-Gorenstein rings established

Sufficient conditions for Gorenstein property derived

Generalization of Evans and Griffith's theorem provided

Abstract

In this paper, after giving a criterion for a Noetherian local ring to be quasi-Gorenstein, we obtain some sufficient conditions for a quasi- Gorenstein ring to be Gorenstein. In the course, we provide a slight generalization of a theorem of Evans and Griffith.