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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.
Xu, A., & Yan, X. (2013). Gorenstein flat and Gorenstein injective dimensions of simple modules. Bulletin of the Iranian Mathematical Society, 39(2), 281-287.
MLA
A. Xu; X. Yan. "Gorenstein flat and Gorenstein injective dimensions of simple modules". Bulletin of the Iranian Mathematical Society, 39, 2, 2013, 281-287.
HARVARD
Xu, A., Yan, X. (2013). 'Gorenstein flat and Gorenstein injective dimensions of simple modules', Bulletin of the Iranian Mathematical Society, 39(2), pp. 281-287.
VANCOUVER
Xu, A., Yan, X. Gorenstein flat and Gorenstein injective dimensions of simple modules. Bulletin of the Iranian Mathematical Society, 2013; 39(2): 281-287.