Following E. Mares [12] and H. Bass [2] we shall first consider a semiperfect module P over a
ring R. One of the important properties of P is the lifting property as follows: Let ί>//(P)= Σ …

1. BACKGROUND We shall use [5] freely; this paper is available at present in preprint form.
We restate now some of its notations and results: N c M means that N is a proper submodule …

The (unital right) module M (over the ring R with identity) is said to have the summand
intersection property if the intersection of any two direct summands of M is a direct …

1. Introduction. Sometimes, a general theorem for a class of abelian groups can be proved
by first showing that the property lives in the en-domorphism rings. Then some theorems are …

The structure of rings such that each of its homomorphic images has the property that each
cyclic right module over it is essentially embeddable in a direct summand is determined …

In [3] C. Faith and EA Walker gave a characterization of a left artinian ring in terms of module
theories. That is, a ring B is left artinian if and only if every injective left B-module is a direct …

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 …

Throughout all rings R are associative wit, h identity, and all modules are unitary right R-
modules. Mod-R will denote the category of unitary right R-modulcs. A classical result in ring …

The concept of generalized uniserial rings was given by Nakayama and have been studied
by many authors. Murase described certain types of generalized uniserial rings in terms of …

1. Introduction. The radical N of a ring R, in which the right (left) ideals satisfy the descending
chain condition, is usually defined as the join of all nil right (left) ideals in R. It is well known …