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.
Categories: math.KT math.RA