Proof. For any ring R with identity, it is easy to see that a right ideal/of R is generated by an
idempotent if and only if/is a direct summand of the right iϋ-module RR. If I is an injective …

In this paper, a new class of rings, called exchange rings, is defined and studied. The class
of exchange rings includes regular rings in the sense of yon Neumann, local rings, and …

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 …

It is shown that, given a module M over a ring with 1, every direct product of copies of M is a
direct sum of modules with local endomorphism rings if and only if every direct sum of copies …

For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if,
whenever N+ X= M with M/X singular, we have X= M. If there exists an epimorphism p: P→ M …

We shall call a ring R a left IF ring if every injective left R-module is flat. The purpose of this
paper is to characterize left and two-sided IF rings in several ways and to give some …

For homological notions the reader is referred to [2]. For the notions, singular submodule,
finite dimensional module, the reader is referred to [7],[8]. For the notion of maximal quotient …

ON THE INJECTIVITY AND FLATNESS OF CERTAIN CYCLIC MODULES Page 1
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 48, Number 1, March …

Idempotents can be lifted modulo a one-sided ideal L of a ring R if, given $ x\in R $ with $ x-
{x^ 2}\in L $, there exists an idempotent $ e\in R $ such that $ ex\in L $. Rings in which …