In 1-4] Nakayama proved that every module M over a generalized uniserial ring has a
decomposition M=~) M~ in which each term is A uniserial (ie, its submodules form a chain) …

It is easy to see that such a decomposition is automatically an indecomposable
decomposition; that is, one in which each term M, is indecomposable. Every semisimple …

First we take a right artinian ring R. Then every injective. R-module E is a direct sum of
indecomposable modules. Further for every simple submodule S of Ey there exists a direct …

ON RINGS WHOSE LEFT MODULES ARE MODULES Page 1 PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 54, January 1976 ON RINGS WHOSE LEFT …

The following conditions are shown to be equivalent: 1) ring A is generalized uniserial (not
necessarily artinian); 2) every finitely presented A module is semiserial; 3) A is semiperfect …

NOTE ON RINGS OF FINITE REPRESENTATION TYPE AND DECOMPOSITIONS OF
MODULES Page 1 PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY …

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 …

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 …

A module is uniserial in case its submodules are linearly ordered by inclusion. A ring R is left
(right) serial if it is a direct sum of uniserial left (right) R-modules. A ring R is serial if it is both …

Generalizing a fundamental property of semisimple modules, Anderson wx and Fuller 1
introduced the following important concept for direct decompositions of modules. A …