G--Gorenstein modules

TL;DR

This paper introduces G-Gorenstein modules over Noetherian rings, characterizes them, and explores their relationship with Gorenstein modules, providing new insights into Gorenstein injective resolutions and ring properties.

Contribution

It defines G-Gorenstein modules via Cousin complexes, characterizes them, and shows they form a broader class than Gorenstein modules, also linking to ring properties.

Findings

G-Gorenstein modules strictly contain Gorenstein modules.

A Gorenstein injective resolution for balanced big Cohen-Macaulay modules is provided.

Characterizations of Gorenstein and regular local rings are obtained.

Abstract

Let $R$ be a commutative Noetherian ring. In this paper, we study those finitely generated $R$-modules whose Cousin complexes provide Gorenstein injective resolutions. We call such a module a G-Gorenstein module. Characterizations of G-Gorenstein modules are given and a class of such modules is determined. It is shown that the class of G-Gorenstein modules strictly contains the class of Gorenstein modules. Also, we provide a Gorenstein injective resolution for a balanced big Cohen-Macaulay $R$-module. Finally, using the notion of a G-Gorenstein module, we obtain characterizations of Gorenstein and regular local rings.