Remarks on Gorenstein weak injective and weak flat modules

TL;DR

This paper introduces broader classes of Gorenstein weak injective and flat modules, explores their properties, and characterizes rings where all modules are Gorenstein weak injective, expanding the understanding of module theory.

Contribution

It defines Gorenstein weak injective and flat modules, compares them to classical classes, and investigates their properties and stability in ring theory.

Findings

Characterization of rings where all modules are Gorenstein weak injective

Relation between weak cosyzygy and Gorenstein weak cosyzygy

Stability results for Gorenstein weak injective modules

Abstract

In this paper, we introduce the notions of Gorenstein weak injective and weak flat modules respectively in terms of weak injective and weak flat modules, which is larger than classical classes of Gorenstein injective and flat modules. In this new setting, we characterize rings over which all modules are Gorenstein weak injective. Moreover, we also discuss a relation between weak cosyzygy and Gorenstein weak cosyzygy of a module, and the stability of Gorenstein weak injective modules.