Let $ R $ be a discrete valuation domain with field of fractions $ Q $ and maximal ideal
generated by $\pi $. Let $\Lambda $ be an $ R $-order such that $ Q\Lambda $ is a …

This dissertation focuses on extending certain notions from Abelian group theory and
module theory over integral domains to modules over non-commutative rings. In particular …

Let $ _RM $ be a nonsingular left $ R $-module whose Morita context is nondegenerate, let
$ B=\operatorname {End} _ {R} M $ and let ${M^*}=\operatorname {Hom} _ {R}(M, R) $. We …

We define a module M to be G r-extending if for each exact submodule X of M there exists a
direct summand D of M such that X∩ D is essential in both X and D. We investigate G r …

The purpose of this paper is to introduce the study of perfect torsion theories on
$\operatorname {Mod} R $ and to dualize the concept of divisible module. A torsion theory …

We generalize the well-known fact that for a pair of Morita equivalent rings R and S their
maximal rings of quotients are again Morita equivalent: If τ n (M) denotes the torsion theory …

In this note, developing our previous work [8] with S. Takashima, we will characterize rings R
for which every finitely generated submodule of the injective envelope E (RR) is torsionless …

Let R be a semiprime, right Goldie ring, with semisimple Artinian right quo-tient ring Q (R). If
M is a right R-module, then the Goldie rank of M, written Grkº M, or Grk M if the context is …

Singular left modules over an associative ring A are characterized by the fact that the
annihilator of every element is an essential left ideal. These modules play an important part …

The study of various types of hulls of a module has been of interest for a long time. Our focus
in this paper is to present results on some classes of these hulls of modules, their examples …