This paper is a loosely connected collection of results on rings and modules. The first
section is concerned with quasi-injective modules of a ring. A module M is said to be quasi …

Let MR denote a right module over a ring R; MR is unital in case B has an identity element
which is the identity operator on M. A module (resp. unital module) MR is injeetive (resp …

QUASI-INJECTIVE AND PSEUDO-INFECTIVE MODULES Page 1 Canad. Math. Bull. Vol. 18
(3), 1975 QUASI-INJECTIVE AND PSEUDO-INFECTIVE MODULES BY SK JAIN AND SURJEET …

Let R be a principal ideal ring with the descending chain condition. Then it is known that any
R-module 1) is a direct sum of cyclic modules. This was apparently first proved by KOTHE …

Introduction In this discussion every module over a ring R will be understood to be a left i2-
module. R will always have a unit, and every module will be unitary. The aim of this paper is …

The object of this paper is to study the relationship between certain projective modules and
their endomorphism rings. Specifically, the basic problem is to describe the projective …

In analogy to the elementwise definition of von Neumann regular rings an $ R $-module $ M
$ is called regular if given any element $ m\in M $ there exists $ f\in {\operatorname {Hom} …

1. Although most of the concepts related to the chain conditions for modules can easily be
dualized, a conspicuous phenomenon of the theory is the lack of a complementary notion to …

6 0 GOEL AND JAIN self-injective ring (or if R is a semiperfect ring) then each cyclic R-
module is a-injective if and only if R is a direct sum of semisimple artinian ring and a finite …

A module A is called an essential extension of a submodule B if BnCFCO for every nonzero
submodule C of A. A module is said to be injective if it is a direct summand of every …