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 …

Several different versions of “factoriality” have been defined for commutative rings with zero
divisors. We apply semigroup theory to study these notions in the context of a commutative …

We introduce and study a nontrivial generalization of uniserial modules and rings. A module
is called weakly uniserial if its submodules are comparable regarding embedding. Also, a …

Let ${} _RM $ be a left $ R $-module whose Morita context is nondegenerate, $ S={\text
{End}}({} _RM) $, and $ N=\operatorname {Hom}({} _RM, R) $. If ${} _RM $ is also …

Although many results concerning Abelian groups carry over to modules over integral
domains, the situation is more complex in the non-commutative case since there are several …

A right R-module MR over any ring R with 1 is called torsion-free if it satisfies the equality for
every r∈ R. An equivalent definition was used by Hattori [11]. We establish various …

If $ R $ is a ring with 1, we call a unital left $ R $-module $ M $ co-Hopfian (Hopfian) in the
category of left $ R $-modules if any monic (epic) endomorphism of $ M $ is an …

Abstract Baer's Criterion for Injectivity is a useful tool of the theory of modules. Its dual
version (DBC) is known to hold for all right perfect rings, but its validity for the non-right …

Let R be a commutative ring with identity and let 𝒬 be the set of finitely generated
semiregular ideals of R. A 𝒬-torsion-free R-module M is called a Lucas module if Ext R 1 …

Let R be an associative ring with identity. A right R-module MR is said to have Property (A), if
each finitely generated ideal I⊆ Z (MR) has a nonzero annihilator in MR. Evans [Zero …