It is shown that, given a module M over a ring with 1, every direct product of copies of M is a
direct sum of modules with local endomorphism rings if and only if every direct sum of copies …

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

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

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 …

Throughout R will represent a ring with unit element 1, and all modules will be unitary 7?-
modules. We call a module M a completely indecomposable module if the endomorphism …

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

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 …

Let M be a left module over a ring R. A submodule N of M is called locally split in M if for
each x EN there exists a homomorphism h: Mt N such that h (x)= x. It is shown that if N is …

This is a study of the conditions under which smallness of proper submodules will influence
the structure of the endomorphism ring of a module. The case in which that endomorphism …

When every projective module is a direct sum of finitely generated modules Page 1 Journal
of Algebra 315 (2007) 454–481 www.elsevier.com/locate/jalgebra When every projective …