Homology theories and Gorenstein dimensions for complexes

L Liang - Algebras and Representation Theory, 2021 - Springer
In this paper, we first study the Gorenstein projective/flat dimension of complexes of
modules. The relation between the Gorenstein projective/flat dimension for complexes and …

Gorenstein homological dimensions of complexes with respect to a semidualizing module

C Zhang, L Wang, Z Liu - Communications in Algebra, 2014 - Taylor & Francis
In this article, we study finite Gorenstein homological dimensions of complexes with respect
to a semidualizing module. A special attention is paid to the dimensions of homologically …

Homology theories for complexes based on flats

L Liang - Glasgow Mathematical Journal, 2021 - cambridge.org
In this paper, we introduce and study the Gorenstein relative homology theory for
unbounded complexes of modules over arbitrary associative rings, which is defined using …

Strongly Gorenstein flat modules and dimensions

N Mahdou, M Tamekkante - Chinese Annals of Mathematics, Series B, 2011 - Springer
There is a variety of nice results about strongly Gorenstein flat modules over coherent rings.
These results are done by Ding, Lie and Mao. The aim of this paper is to generalize some of …

On the finiteness of Gorenstein homological dimensions

I Emmanouil - Journal of Algebra, 2012 - Elsevier
In this paper, we study certain properties of modules of finite Gorenstein projective, injective
and flat dimensions. We examine conditions which imply that all Gorenstein projective …

Gorenstein dimensions over ring homomorphisms

W Dejun - Communications in Algebra, 2015 - Taylor & Francis
In this paper, we study injective dimension and Gorenstein injective dimension over local
ring homomorphisms. Some well-known results are generalized. For example, the Bass …

Complete cohomology for complexes with finite Gorenstein AC-projective dimension

J Hu, Y Geng, Q Jiang - Frontiers of Mathematics in China, 2016 - Springer
We study complete cohomology of complexes with finite Gorenstein AC-projective
dimension. We show first that the class of complexes admitting a complete level resolution is …

Strongly Gorenstein flat dimensions of complexes

Z Wang, Z Liu - Communications in Algebra, 2016 - Taylor & Francis
In this article, we define and study a notion of strongly Gorenstein flat dimensions for
complexes of left modules over associative rings. In particular, we consider the class of …

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 …

Gorenstein injective and Gorenstein flat dimensions under base change

L Khatami, S Yassemi - Communications in Algebra, 2003 - Taylor & Francis
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