On Gruenberg Resolutions for Augmented Algebras.
On long exact -sequences in module theory.
On projective resolutions of flat modules
On relative extension groups in the category of commutative diagrams.
On the Bernstein-Gelfand-Gelfand resolution and the Duflo sum formula
On the Buchsbaum-Eisenbud theory of finite free resolutions.
On the deviations of a local ring.
On the equivalence of Quillen's and Swan's -theories.
On the geometry of intuitionistic S4 proofs.
On the homology of small categories and asynchronous transition systems.
One-sided Gorenstein subcategories
We introduce the right (left) Gorenstein subcategory relative to an additive subcategory of an abelian category , and prove that the right Gorenstein subcategory is closed under extensions, kernels of epimorphisms, direct summands and finite direct sums. When is self-orthogonal, we give a characterization for objects in , and prove that any object in with finite -projective dimension is isomorphic to a kernel (or a cokernel) of a morphism from an object in with finite -projective dimension...
Orientations and multiplicative structures of resolutions.
Projective covers and minimal free resolutions.
Projective Modules over Graded Lie Algebras. I.
Projective resolutions of representations of GL (n).
Quasi resolved semigroups and quintets.
Realization of long exact sequences of abelian groups.
Given a long exact sequence of abelian groupsL: ... → Li-1 →ξi-1 Li →ξi Li+1 → ...a short exact sequence of complexes of free abelian groups is constructed whose cohomology long exact sequence is precisely L. In this sense, L is realized. Two techniques which are introduced to reduce or replace lengthy diagram chasing arguments may be of interest to some readers. One is an arithmetic of bicartesian squares; the other is the use of the fact that categories of morphisms of abelian categories...
Resolutions by Polygraphs.
Semi-infinite homological algebra.
Sobre resolubilidad en una categoría de Burgin.
En un trabajo de Huq se introduce el concepto de resolubilidad en categorías [2]. En mi tesis doctoral [1 (4.2.3), p.87] se hace distinción entre resolubilidad fuerte (resolubilidad de Huq) y resolubilidad, conceptos que coinciden en el caso de grupos, anillos asociativos y álgebras de Lie, pero no en cualquier tipo de Ω-grupos, donde la resolubilidad corresponde a la introducida en [1].El objeto de esta nota es dar una caracterización de los objetos resolubles (corolario 6), la cual nos permite...