Gorenstein flat and Gorenstein injective dimensions of simple modules
نویسندگان
چکیده مقاله:
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.
منابع مشابه
Gorenstein Flat and Gorenstein Injective Dimensions of Simple Modules
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 Gorenstein flat dimension of R/I as a right R-module and the Gorenstein injective dimension of R/I as a left R-module are identical. In particular, we show that for a simple module S over a commutative Gorenstein ring R, the G...
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عنوان ژورنال
دوره 39 شماره 2
صفحات 281- 287
تاریخ انتشار 2013-05-15
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