1. Introduction, In this paper we prove several theorems about rings having a generous
supply of projective injective modules. This is a curious class of rings. For instance, every …

Let R be an integral domain in which all finitely generated ideals are principal. Let M be a
projective R-module. It is well known that if M is finitely generated it is free. By a familiar …

Let A be an associative ring which possesses a unit element t and. satisfies the minimum
condition for left ideals. Recently NAGAO-NAKAYA~ IA [9] have determined the structure of …

Abstract A right R-module M is said to be finendo provided that as a left module over its
endomorphism ring it is finitely generated. Let B= End MR. Then B n→ M→ 0 is exact for …

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 …

When every projective module is a direct sum of finitely generated modules Page 1 Journal
of Algebra 315 (2007) 454–481 www.elsevier.com/locate/jalgebra When every projective …

M commutes. The first section of this paper contains results which are needed to prove a
decomposition theorem for quasi-projective modules over left perfect rings (Theorem 1.10) …

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 …

First published in 1982. These lectures are in two parts. Part I, entitled injective Modules
Over Levitzki Rings, studies an injective module E and chain conditions on the set A^(E, R) …

In this note all rings are commutative and all modules are unital. Let R be a ring. An R-
module M is called a multiplication module if for every submodule N of M there exists an …