On the existence of certain modules of finite Gorenstein homological   dimensions
  Let (R,m) be a commutative Noetherian local ring. It is known that R is Cohen-Macaulay if there exists either a nonzero finitely generated R-module of finite injective dimension or a nonzero Cohen-Macaulay R-module of finite projective dimension. In this paper, we investigate the Gorenstein analogues of these facts. 
Kamran Divaani-Aazar, Fatemeh Mohammadi Aghjeh Mashhad and Massoud   Tousi
math.AC