We investigate several homological aspects of recollements of abelian categories. In
particular, we study how various homological invariants and dimensions of the categories …

We consider the question of whether the injective modules generate the unbounded derived
category of a ring as a triangulated category with arbitrary coproducts. We give an example …

A detailed study is made of super elliptic curves, namely super Riemann surfaces of genus
one considered as algebraic varieties, particularly their relation with their Picard groups …

In 2005, the second author and Todorov introduced an upper bound on the finitistic
dimension of an Artin algebra, now known as the ϕ ϕ-dimension. The ϕ ϕ-dimension …

Repetitiveness in projective and injective resolutions and its influence on homological
dimensions are studied. Some variations on the theme of repetitiveness are introduced, and …

In this work, we will prove various results concerning the non-commutative main conjecture
of Iwasawa theory both for function fields and for totally real fields. We build upon the …

During the last several years, Artin, Jørgensen, Stafford, Yekutieli, and others have
generalized many homological results from the commutative case to the noncommutative …

Let ${\frak g} $ be a finite dimensional Lie superalgebra over a field of characteristic zero.
Let $ U ({\frak g}) $ be the enveloping algebra of ${\frak g} $. We show that when ${\frak g} …

Let k be a commutative ring, R be a k-algebra, G be a group acting as k-algebra
automorphisms on R, with the action of g EG on r ER written as rg, and S= RG={r RI rg= r for …

A left R-module RM is said to have an injective resolution with a redundant (strongly
redundant) image from an integer n> 1 in case the nth cosyzygy 52, has a decomposition fl …