The snake lemma in an abelian category with enough projectives (Injectives)

The Snake Lemma, fundamental in producing long exact sequences in homology or cohomology theories based on an abelian category, is shown to have a proof formally identical to the familiar one involving abelian groups when the category either has enough projectives or enough injectives.     

Inductions and restrictions on towers of cellularly stratified diagram algebras

Hartmann et al. defined the concept of cellularly stratified algebras that combine the features of both cellular algebras and stratified algebras. Many important diagram algebras in mathematics and physics, such as some Brauer, partition and BMW algebras, are cellularly stratified algebras, and each of these forms a tower of algebras. This article gives the concept of towers of cellularly stratified algebras in an axiomatic manner, and studies it in terms of induction and restriction functors. In particular, for certain towers of cellularly stratified algebras, we provide a criterion for semi-simplicity by using the cohomology groups of cell modules.     

Generalization of Regular Modules

We study generalizations of regular modules by Ramamurthy and Mabuchi. These are also generalizations of fully right idempotent and fully left idempotent rings, respectively. We also define and study the properties of *-weakly regular modules, a generalization of fully idempotent rings.     

On QB Endomorphism Rings

We study, in this article, QB endomorphism rings of quasi-projective modules by means of completions of diagrams. The dual problems for quasi-injective modules are also investigated.     

Endomorphism Rings of Regular Modules over Wild Hereditary Algebras

Let X be an indecomposable regular module over a connected wild hereditary path-algebra. The main result is a factorization property for maps in the radical of End _H (X) and an upper bound for its degree of nilpotency. The bound is sharp if X has elementary quasi-top. In this, case the socle of End _H (X) can also be characterized.     

Various Classes of Pseudoprojective Modules over Semiperfect Rings

We give the structure of a class of pseudoprojective modules over a semiperfect ring. Moreover, we describe all self-pseudoprojective modules over an Artinian serial ring. As an application, we give the number of (non-necessarily hereditary) torsion theories over such a ring.     

Uniform Annihilation of Local Cohomology Modules Over a Gorenstein Ring

In this article, by using the theory of Gorenstien dimension, we study the uniform annihilation theorem for local cohomology modules over a (not necessary finite dimensional) Noetherian Gorenstein ring.     

Doi–Hopf Modules and Yetter–Drinfeld Modules for Quasi-Hopf Algebras

For a quasi-Hopf algebra H, a left H-comodule algebra  and a right H-module coalgebra C we will characterize the category of Doi–Hopf modules ^C ?(H) in terms of modules. We will also show that for an H-bicomodule algebra  and an H-bimodule coalgebra C the category of generalized Yetter–Drinfeld modules (H) ^C is isomorphic to a certain category of Doi–Hopf modules. Using this isomorphism we will transport the properties from the category of Doi–Hopf modules to the category of generalized Yetter–Drinfeld modules.