Stability of strongly Gorenstein flat modules

TL;DR

This paper proves that two-degree Ding projective modules are equivalent to Ding projective modules, clarifying their stability properties within module theory.

Contribution

It establishes the equality of two-degree Ding projective modules and Ding projective modules, contributing to the understanding of their stability.

Findings

Two-degree Ding projective modules are the same as Ding projective modules.

The result simplifies the classification of these modules.

Provides insight into the structure of Gorenstein flat modules.

Abstract

A left $R$-module $M$ is called two-degree Ding projective if there exists an exact sequence $...\longrightarrow D_{1}\longrightarrow D_{0}\longrightarrow D_{-1}\longrightarrow D_{-2}\longrightarrow...$ of Ding projective left $R$-modules such that $M\cong\ker (D_{0}\longrightarrow D_{-1})$ and $\Hom_{R} (-, F)$ leaves the sequence exact for any flat (or Gorenstein flat) left $R$-module $F$. In this paper, we show that the two-degree Ding projective modules are nothing more than the Ding projective modules.