Bulletin of the
Korean Mathematical Society BKMS

Let $R$ be a Ding-Chen ring. Yang \cite{Yang2012} and Zhang \cite{Zhang2015} asked whether or not every $R$-module has finite Ding projective or Ding injective dimension. In this paper, we give a new characterization of that all modul\-es have finite Ding projective and Ding injective dimension in terms of the relationship between Ding projective and Gorenstein flat modules. We also give an example to obtain negative answer to the above question.

Keywords: Ding projective module, Gorenstein flat module, Ding-Chen ring

MSC numbers: 16E65, 18G20, 18G25