Gorenstein flat and Gorenstein injective dimensions of simple modules

Authors

  • A. Xu Department of Mathematics, Nanjing University
  • X. Yan 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.

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Journal title

volume 39  issue 2

pages  281- 287

publication date 2013-05-15

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