We define and study a notion of Gorenstein projective dimension for complexes of left
modules over associative rings. For complexes of finite Gorenstein projective dimension we …

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 …

We study finitely generated modules has finite projective dimension. Comparison
morphisms and link these functors. We give a self-contained treatment of modules of finite G …

In this paper we study relative and Tate cohomology of modules of finite Gorenstein injective
dimension. Using these cohomology theories, we present variations of Grothendieck local …

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 …

Cohen-Macaulay dimension for modules over a commutative ring has been defined by AA
Gerko. That is a homological invariant sharing many properties with projective dimension …

Ascent Properties of Auslander Categories Page 1 Canad. J. Math. Vol. 61 (1), 2009 pp. 76–108
Ascent Properties of Auslander Categories Lars Winther Christensen and Henrik Holm Abstract …

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 …

Over any associative ring $ R $ it is standard to derive $\mathrm {Hom} _R (-,-) $ using
projective resolutions in the first variable, or injective resolutions in the second variable, and …

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 …