Let R be a ring, M a left R-module, I an infinite set, N either the direct sum or product of| I|
copies of M, and E the endomorphism ring of N as a left R-module. In this note it is shown …

Let R be an associative ring with identity. We show that every direct sum of singular injective
right R-modules is injective iff any one of the following equivalent conditions holds. i) Every …

Classically, there has been, for obvious reasons, an intimate relation between the concepts"
rings of quotients" and" divisible modules". Recently, however, their generalizations have …

Decomposability of modules into a direct sum of ideals Page 1 LITERATURE CITED i. W. Feit,
Characters of Finite Groups, Benjamin, New York (1967). 2. D. Gorenstein, Finite Groups …

1. Introduction. As is well known, any two faithful modules over a simple ring are isomorphic
if their endomorphism rings are isomorphic. This theorem, however, cannot be extended to …

Mathematical Journal of Okayama University Page 1 Mathematical Journal of Okayama
University Volume 51, Issue 1 2009 Article 6 A NOTE ON ALMOST INJECTIVE MODULES …

1. It has been shown by Feller and Swokowski [I] that if R is an integral domain which has a
right and left quotient ring, then the endomorphism ring E (M) of a finitely generated torsion …

Theorem 1. Let R be the endomorphism ring of a left module^ N, where either Ν is a
distributive module that decomposes into a direct sum of quasi-injective modules, or Ν is a …

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 …

Cukerman [2], Shanny [5], and Ware [7] have shown that a ring R is Artin semisimple if and
only if R has a nonfinitely generated free module with regular endomorphism ring. This …