Este documento constituye la memoria de tesis doctoral para optar al grado de Doctor en
Matemáticas. Este trabajo lo dividimos en dos bloques. En el primer bloque, Capítulos 3 y 4 …

En el primer bloque, Capítulos 3 y 4, cuyo ámbito de trabajo es una categoría abeliana con
suficientes inyectivos, consideramos X e Y dos subcategorías plenas de la categoría …

Recently, Gorenstein dimensions relative to a semidualizing module have been the subject
of numerous studies with interesting extensions of the classical homological dimensions …

In this paper we develop the homological properties of the Gorenstein $(\Le,\A) $-flat $ R $-
modules $\GF_ {(\Flat (R),\A)} $ proposed by Gillespie,\linebreak where the class …

Let 𝒜 be an abelian category. In this paper, we investigate the global (𝒳, 𝒴)-Gorenstein
projective dimension gl. GPD (𝒳, 𝒴)(𝒜), associated to a GP-admissible pair (𝒳, 𝒴). We give …

We develop a theory of G-dimension over local homomorphisms which encompasses the
classical theory of G-dimension for finitely generated modules over local rings. As an …

X-Gorenstein Projective Modules Page 1 International Scholarly Research Network ISRN
Algebra Volume 2011, Article ID 270814, 10 pages doi:10.5402/2011/270814 Research Article …

Bourbaki [1] defined A-dimension using finite presentations. In this paper, we extend this
definition by replacing finite presentations with resolutions obtained by using either r …

A new homological dimension, called G*-dimension, is defined for every finitely generated
module M over a local noetherian ring R. It is modeled on the CI-dimension of Avramov …

Let $\A $ be an abelian category, and $\V $, $\W $ two additive full subcategories of $\A $.
We introduce and study the $\V\W $-Gorenstein subcategory of $\A $, which unifies many …