نتایج جستجو برای: Gorenstein flat dimension

تعداد نتایج: 169691  

Journal: :bulletin of the iranian mathematical society 2013
a. xu x. yan

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, ...

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, ...

2008
Driss Bennis

Unlike the Gorenstein projective and injective dimensions, the majority of results on the Gorenstein flat dimension have been established only over Noetherian (or coherent) rings. Naturally, one would like to generalize these results to any associative ring. In this direction, we show that the Gorenstein flat dimension is a refinement of the classical flat dimension over any ring; and we invest...

2013
A. XU X. YAN Siamak Yassemi

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...

2009
Edgar E. Enochs Zhaoyong Huang

In terms of the duality property of injective preenvelopes and flat precovers, we get an equivalent characterization of left Noetherian rings. For a left and right Noetherian ring R, we prove that the flat dimension of the injective envelope of any (Gorenstein) flat left R-module is at most the flat dimension of the injective envelope of RR. Then we get that the injective envelope of RR is (Gor...

2008
Driss Bennis D. Bennis

A ring R is called left GF-closed, if the class of all Gorenstein flat left Rmodules is closed under extensions. The class of left GF-closed rings includes strictly the one of right coherent rings and the one of rings of finite weak dimension. In this paper, we investigate the Gorenstein flat dimension over left GF-closed rings. Namely, we generalize the fact that the class of all Gorenstein fl...

2009
Driss Bennis D. Bennis

This paper is a continuation of the papers J. Pure Appl. Algebra, 210 (2007), 437–445 and J. Algebra Appl., 8 (2009), 219–227. Namely, we introduce and study a doubly filtered set of classes of modules of finite Gorenstein projective dimension, which are called (n, m)-strongly Gorenstein projective ((n, m)-SG-projective for short) for integers n ≥ 1 and m ≥ 0. We are mainly interested in studyi...

2007
N. MAHDOU

In this paper, we prove that the global Gorenstein projective dimension of a ring R is equal to the global Gorenstein injective dimension of R, and that the global Gorenstein flat dimension of R is smaller than the common value of the terms of this equality.

Journal: :Kyoto Journal of Mathematics 2009

2005
LARS WINTHER

Given a homomorphism of commutative noetherian rings R → S and an S–module N , it is proved that the Gorenstein flat dimension of N over R, when finite, may be computed locally over S. When, in addition, the homomorphism is local and N is finitely generated over S, the Gorenstein flat dimension equals sup {m ∈ Z | Torm(E,N) 6= 0}, where E is the injective hull of the residue field of R. This re...

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