Bulletin of the Iranian Mathematical Society

Bulletin of the Iranian Mathematical Society

Gorenstein flat and Gorenstein injective dimensions of simple modules

Document Type : Research Paper

Authors
A. Xu 1
X. Yan 2
1 Department of Mathematics, Nanjing University
2 School of Mathematics & Information Technology, Nanjing Xiaozhuang University
Abstract
Let R be a right GF-closed ring with finite left and right
Gorenstein global dimension. We prove that if I is an ideal of
R such that R/I is a semi-simple ring, then the Gorensntein flat
dimensnion of R/I as a right R-module and the Gorensntein
injective dimensnnion of R/I as a left R-module are identical.
In particular, we show that for a simple module S over a
commutative Gorensntein ring R, the Gorenstein flat dimension of
S equals to the Gorenstein injective dimension of S.
Keywords
Gorenstein flat dimension
Gorenstein injective dimension
simple module
Subjects

  • Receive Date 30 July 2011
  • Revise Date 30 January 2012
  • Accept Date 12 April 2012