EXCELLENT EXTENSIONS AND GORENSTEIN HOMOLOGICAL DIMENSION

Let R be a ring and San excellent extension of R. In this paper we study the Gorenstein homological dimensions over Rand S. We show that if M is an S-module, then MR is Gorenstein projective if and only if M-S is Gorenstein projective. Secondly,we prove that the right Gorenstein dimension of R is equal to the right Gorenstein dimension of S. Some results in[4]and[6]are extended to the settings of Gorenstein projective modules and Gorenstein projective dimensions, respectively.