Gorenstein flat and Gorenstein injective dimensions of simple modules

Document Type: Research Paper


1 Department of Mathematics, Nanjing University

2 School of Mathematics & Information Technology, Nanjing Xiaozhuang University


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.


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