Introduction* The concept of the" injective envelope" of a module was first given by Eckmann
and Schopf [2], although this terminology was first employed by Matlis [5]. The injective …

IYTRODCCTION 1: n~ onorphism rings of various types of modules have been objects of
extensive study in the recent past [2, 11, 14, 15, 18, 25, 261. In [15] Erika Mares introduced …

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 notion of secondary representation is in some sense dual to that of primary
decomposition. A module M over the ring A (always assumed to be a com mutative …

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 …

Introduction. This note investigates modules containing an essential direct sum of uniform
submodules. Theorem I gives five different necessary and sufficient conditions in order for a …

Semi-perfect and perfect modules were introduced by Mares [3] as generalizations of
Bass'[2] notions of semi-perfect and perfect rings. She developed a substantial structure …

1. In this paper, the structure theorems of I~ AGAO and l~ AXAYAMA [4] for projective and
injective modules over certain rings are derived by methods different from those used in [4] …

Let E be a ring with identity and M a unitary right^-module wich is a directsum of
indecomposable, infective modules. E. Matlis [13] posed the following question: for any …

Rosenberg and Zelinsky [6] first addressed the question of characterizing for a ring R those
simple modules RT having injective hulls of finite length. In that work they also announced a …