Publisher Summary This chapter provides an overview of the basic concepts of the Krull-
Schmidt theorem. The two proofs of the Krull-Schmidt-Azumaya theorem, mention …

A module is uniserial if its submodules are linearly ordered by inclusion and it is serial if it is
a direct sum of uniserial submodules. This note is a study of rings whose finitely generated …

One of the fundamental problems in the theory of rings is to characterize the rings of
bounded representations type in terms of their structure. The problem has been solved for …

Let ${R_0} $ be a skew field, or more generally, a finite product of full matrix rings over skew
fields. Let ${({R_\lambda}) _ {\lambda\in\Lambda}} $ be a family of faithful ${R_0} $ rings …

1. Throughout this note, all rings will have unit elements and all modules will be unitary. By a
Noetherian ring, we shall mean a right Noetherian ring. A non-zero right ideal in a ring will …

\S 0. Introduction. The main purpose of this paper is to extend some results on completely
reducible modules to quasi-injective modules by replacing “irreducible submodules” with …

Throughout this paper we suppose that all rings and modules are unitary. By J we denote
always the Jacobson radical of a ring S. The left (right, resp.) annihilator of X is denoted by Z …

In a recent paper, Aydoǧdu and López-Permouth have defined a module M to be N-
subinjective if every homomorphism N→ M extends to some E (N)→ M, where E (N) is the …

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 …

It is shown that if R is a commutative ring such that any R-module is a direct sum of
indecomposable modules, then R is an Artinian principal ideal ring (so that every module is …