Gorenstein injective modules and local cohomology
نویسندگان
چکیده
منابع مشابه
Local Cohomology and Gorenstein Injective Dimension over Local Homomorphisms
Let φ : (R, m)→ (S, n) be a local homomorphism of commutative noetherian local rings. Suppose that M is a finitely generated S-module. A generalization of Grothendieck’s non-vanishing theorem is proved for M (i.e. the Krull dimension of M over R is the greatest integer i for which the ith local cohomology module of M with respect to m, Hi m(M), is non-zero). It is also proved that the Gorenstei...
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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, ...
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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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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2004
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-04-07461-1