Characterization of almost Gorenstein rings in terms of the trace ideal

TL;DR

This paper characterizes one-dimensional almost Gorenstein rings using trace ideals and explores their properties in specific $Z_2$-graded rings, advancing understanding of their algebraic structure.

Contribution

It introduces a new characterization of almost Gorenstein rings via trace ideals and applies this to $Z_2$-graded rings, providing novel insights.

Findings

Characterization of one-dimensional almost Gorenstein rings using trace ideals

Analysis of the almost Gorenstein property in $Z_2$-graded rings

New criteria for identifying almost Gorenstein rings

Abstract

We provide a characterization of one-dimensional almost Gorenstein rings in terms of the trace ideal. As an application, we investigate the almost Gorenstein property of certain $\mathbb{Z}_2$-graded rings.