Gorenstein homological dimensions are refinements of the classical homological
dimensions, and finiteness singles out modules with amenable properties reflecting those of …

A semi-dualizing module over a commutative noetherian ring A is a finitely generated
module C with RHomA (C, C)≃ A in the derived category D (A). We show how each such …

We show that an iteration of the procedure used to define the Gorenstein projective modules
over a commutative ring R yields exactly the Gorenstein projective modules. Specifically …

" Ha habido muy pocas exposiciones sistemáticas de la teoría de las categorías derivadas
desde su inicio en el trabajo de Grothendieck y Verdier en la década de 1960. Este libro es …

We use torsion pairs in stable categories and cotorsion pairs in modules categories to study,
in general infinitely generated, Cohen–Macaulay modules and (a generalization of) …

We introduce and investigate the notion of 𝐺𝐶-projective modules over (possibly non-
Noetherian) commutative rings, where 𝐶 is a semidualizing module. This extends Holm and …

We introduce the notion of a duality pair and demonstrate how the left half of such a pair is"
often" covering and preenveloping. As an application, we generalize a result by Enochs et …

Let W be a self-orthogonal class of left R-modules. We introduce and study W-Gorenstein
modules as a common generalization of some known modules such as Gorenstein …

We introduce a new notion of commutative noetherian local rings, which we call dominant.
We explore fundamental properties of dominant local rings and compare them with other …

Consider a non-trivial fiber product $ R= S\times _kT $ of local rings $ S $, $ T $ with
common residue field $ k $. Given two finitely generated $ R $-modules $ M $ and $ N $, we …