In this note, we study rings over which every left module is a direct sum of finitely generated
modules. Chase [5] showed that all such rings are left artinian and Fuller [8] proved that …

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 …

We have given, in [5], a characterization of a right (upper) serial ring in terms of submodules
of finite direct sums of serial modules. In this paper we shall replace the serial module by …

ABSTRACT A canonical form for a module M over a commutative ring R is a decomposition
M£ R/^©••• 0#//„, where the Ij are ideals oiR and Ix£•••£/„. A complete structure theory is …

We have studied the Hiking property on a direct sum of completely indecomposable and
cyclic hollow modules over a ring R in [8]. In this note, we shall define the lifting property of …

The paper is a study of modules with a local endomorphism ring. We consider
decompositions of modules and give a simple proof of Azumaya's theorem. We also define …

A module over a ring is said to be completely decomposable if it is a direct sum of
indecomposable injective submodules. It was proposed by E. Matlis [5] a problem whether …

MODULES WITH PERFECT DECOMPOSITIONS Page 1 MATH. SCAND. 98 (2006), 19^)3
MODULES WITH PERFECT DECOMPOSITIONS LIDIA ANGELERIHUGEL and MANUEL …

Throughout this paper R will denote an associative ring with an identity and R-modules will
always be right, unital R-modules.~ R will denote the class of all right, unital R-modules and …

Given a commutative ring S and the proper subring R of S, it is shown that if each proper
subring of S containing R is Artinian, then S is Artinian. Examples are given to show that the …