Chapter 1 covers the background necessary for what follows. In particular, general
properties of injectivity and some of its well-known generalizations are stated. Chapter 2 is …

ABSTRACT A widely used result of Wedderburn and Artin states that “every left ideal of a
ring R is a direct summand of R if and only if R has a unique decomposition as a finite direct …

Modules for which every submodule has a unique closure Page 317 302 MODULES FOR
WHICH EVERY SUB MODULE HAS A UNIQUE CLOSURE PATRICK F. SMITH Department of …

NONSINGULAR EXTENDING MODULES Page 1 NONSINGULAR EXTENDING MODULES
PATRICK F. SMITH ABSTRACT. In this paper, it is shown that if R is a semiprime right Goldie …

Let R be a clean ring with an ideal I such that R/I is semiperfect and K0 (I) is torsion-free. We
prove that, under some mild conditions, units in R/I can be lifted to units in R. This implies …

It is known that every essential extension of a direct sum of injective hulls of simple R-
modules is a direct sum of injective R-modules if and only if the ring R is right noetherian …

Let△ be a multiplicatively closed set of finitely generated nonzero ideals of a ring R. Then
the concept of a△-reduction of an R-submodule D of an R-module A is introduced and …

A submodule N of a right R-module M is called coneat if for every simple right R-module S,
any homomorphism $ N {\rightarrow} S $ can be extended to a homomorphism $ M …

A module $ M $ is said to be coretractable if there exists a nonzero homomorphism of every
nonzero factor of $ M $ into $ M $. We prove that all right (left) modules over a ring are …

We study weak relative injective and relative tight modules in the category u [M], where M is
a right R-module. Many of the known results in the category of right R-modules are extended …