This paper consists of three parts. The first is devoted to investigating the equivalence and
left-right symmetry of several conditions known to characterize finite dimensional algebras …

We study torsion torsionfree (= TTF) triples in abelian and triangulated categories.(Notice
that TTF triples in a triangulated category are essentially in bijection with recollement data …

In his work [26], SE Dickson defined the notion of torsion theory (now called torsion pair) in
the general framework of abelian categories, which generalizes the concept of …

A ring R is called a right Harada ring if it is right Artinian and every non-small right R-module
contains a non-zero injective submodule. The first result in our paper is the following: Let R …

We study when the stable category \mathcalA/⟨\mathcalT⟩ of an abelian category
\mathcalA modulo a full additive subcategory \mathcalT is balanced and, in case \mathcalT …

This paper is a study of nonsingular rings with essential socles. These rings were first
investigated by Goldie [5] who studied the Artinian case and showed that an …

Let R be a ring which is associative and its radical be N. A ring R is called semilocal if R/N is
semisimple. Mochizuki [5] studied the double centralizer of a minimal faithful R-module for …

We study when the stable category. 4/(T) of an abelian category. A modulo. a full additive
subcategory T is balanced and, in case T is functorially finite in. 4, we study a weak version …

ON MATRIX METHODS IN RING THEORY George Ivanov A Thesis For the Degree of Doctor of
Philosophy Submitted to The Australian Natio Page 1 ON MATRIX METHODS IN RING …