A refinement of Gorenstein flat dimension via the flat–cotorsion theory
We introduce a refinement of the Gorenstein flat dimension for complexes over an
associative ring—the Gorenstein flat-cotorsion dimension—and prove that it, unlike the …
associative ring—the Gorenstein flat-cotorsion dimension—and prove that it, unlike the …
A note on Gorenstein flat dimension
D Bennis - Algebra Colloquium, 2011 - World Scientific
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 …
Gorenstein flat dimension have been established only over Noetherian (or coherent) rings …
Gorenstein flat dimension of complexes
A Iacob - Journal of mathematics of Kyoto University, 2009 - projecteuclid.org
We define a notion of Gorenstein flat dimension for unbounded complexes over left GF-
closed rings. Over Gorenstein rings we introduce a notion of Gorenstein cohomology for …
closed rings. Over Gorenstein rings we introduce a notion of Gorenstein cohomology for …
[HTML][HTML] Transfer of Gorenstein dimensions along ring homomorphisms
LW Christensen, S Sather-Wagstaff - Journal of Pure and Applied Algebra, 2010 - Elsevier
A central problem in the theory of Gorenstein dimensions over commutative noetherian rings
is to find resolution-free characterizations of the modules for which these invariants are finite …
is to find resolution-free characterizations of the modules for which these invariants are finite …
Gorenstein global dimensions and cotorsion dimension of rings
D Bennis, N Mahdou - Communications in Algebra, 2009 - Taylor & Francis
In this article, we establish, as a generalization of a result on the classical homological
dimensions of commutative rings, an upper bound on the Gorenstein global dimension of …
dimensions of commutative rings, an upper bound on the Gorenstein global dimension of …
[HTML][HTML] Gorenstein homological dimensions
H Holm - Journal of pure and applied algebra, 2004 - Elsevier
In basic homological algebra, the projective, injective and flat dimensions of modules play
an important and fundamental role. In this paper, the closely related Gorenstein projective …
an important and fundamental role. In this paper, the closely related Gorenstein projective …
Transfer of Gorenstein dimensions of unbounded complexes along ring homomorphisms
L Zhongkui, R Wei - Communications in Algebra, 2014 - Taylor & Francis
Let R→ S be a ring homomorphism. We consider the relationships of the Gorenstein
dimensions of an R-complex X (possibly unbounded) with those of the S-complexes R Hom …
dimensions of an R-complex X (possibly unbounded) with those of the S-complexes R Hom …
On Gorenstein projective, injective and flat dimensions-a functorial description with applications
LW Christensen, A Frankild, H Holm - arXiv preprint math/0403156, 2004 - arxiv.org
Gorenstein homological dimensions are refinements of the classical homological
dimensions, and finiteness singles out modules with amenable properties reflecting those of …
dimensions, and finiteness singles out modules with amenable properties reflecting those of …
Gorenstein projective, injective, and flat complexes
X Yang, Z Liu - Communications in Algebra, 2011 - Taylor & Francis
Enochs and Jenda gave some characterizations of Gorenstein injective and projective
complexes over n-Gorenstein rings. The aim of this article is to generalize these results and …
complexes over n-Gorenstein rings. The aim of this article is to generalize these results and …
On Gorenstein flat dimension
S Bouchiba - Journal of Algebra and its Applications, 2015 - World Scientific
The theory of Gorenstein flat dimension is not complete since it is not yet known whether the
category 𝒢ℱ (R) of Gorenstein flat modules over a ring R is projectively resolving or not …
category 𝒢ℱ (R) of Gorenstein flat modules over a ring R is projectively resolving or not …