In 1966, Auslander introduced the notion of the G-dimension of a finitely generated module over a Cohen-Macaulay noetherian ring and found the basic properties of these dimensions. His results were… (More)

In the general setting of Grothendieck categories with enough projectives, we prove theorems that make possible to restrict the study of the problem of the existence of -covers and envelopes to the… (More)

In this paper, we show the existence of copure injective preenvelopes over noetherian rings and copure flat preenvelopes over commutative artinian rings. We use this to characterize n-Gorenstein… (More)

We will generalize the projective model structure in the category of unbounded complexes of modules over a commutative ring to the category of unbounded complexes of quasi-coherent sheaves over the… (More)

We study Gorenstein categories. We show that such a category has Tate cohomological functors and Avramov-Martsinkovsky exact sequences connecting the Gorenstein relative, the absolute and the Tate… (More)

We consider rings admitting a Matlis dualizing module E. We argue that if R admits two such dualizing modules, then a module is reflexive with respect to one if and only if it is reflexive with… (More)

Preliminaries. Bn (resp. 5„_i) will denote the subset of Rn consisting of those x such that ||x|| g 1 (resp. ¡|x|| = 1). x0 will denote the point (1, 0, 0, •• -, 0) of R" and T will denote Si made… (More)

The coGalois group associated to a torsion free cover of a Z-module are known to have a canonical topology. In this paper we will see that this topology can be deduced by p-roots of elements of… (More)

The principle “Every result in classical homological algebra should have a counterpart in Gorenstein homological algebra” is given in [3]. There is a remarkable body of evidence supporting this claim… (More)