$n$-Strongly Gorenstein Projective, Injective and Flat modules

TL;DR

This paper explores the relationships and homological properties of various classes of $n$-strongly Gorenstein modules, including projective, injective, and flat modules, and introduces the concept of $n$-strongly Gorenstein flat modules.

Contribution

It introduces the notion of $n$-strongly Gorenstein flat modules and studies their properties and relations to existing $n$-strongly Gorenstein projective and injective modules.

Findings

Established relations between $m$- and $n$-strongly Gorenstein modules for different $m$ and $n$.

Analyzed the homological behavior of $n$-strongly Gorenstein flat modules.

Connected $n$-strongly Gorenstein flat modules with projective and injective counterparts.

Abstract

In this paper, we study the relation between $m$-strongly Gorenstein projective (resp. injective) modules and $n$-strongly Gorenstein projective (resp. injective) modules whenever $m \neq n$, and the homological behavior of $n$-strongly Gorenstein projective (resp. injective) modules. We introduce the notion of $n$-strongly Gorenstein flat modules. Then we study the homological behavior of $n$-strongly Gorenstein flat modules, and the relation between these modules and $n$-strongly Gorenstein projective (resp. injective) modules.