As a proper generalization of injective modules in term of supplements, we say that a
module M has the property (SE)(respectively, the property (SSE)) if, whenever M (N, M has a …

Rings Whose Modules Are {oplus}-Supplemented Page 1 Ž . Journal of Algebra 218, 470487
1999 Article ID jabr.1998.7830, available online at http:rrwww.idealibrary.com on Rings Whose …

For a ring A, it is proved that all A-modules are semiregular if and only if A is an Artinian
serial ring and J2(A)= 0. All rings are assumed to be associative and with nonzero identity …

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 …

Let R be a commutative ring with nonzero identity. Our objective is to investigate
representable modules and to examine in particular when submodules of such modules are …

We provide some characterizations of rings R for which every (finitely generated) module
belonging to a class C of R-modules is a direct sum of cyclic submodules. We focus on the …

A module satisfying the descending chain condition on cyclic submodules is called
coperfect. The class of coperfect modules lies properly between the class of locally artinian …

163 NONZERO INJECTIVE COVERS OF MODULES Richard Belshoff and Jinzhong Xu
Abstract. We show that if R is a ring such that every n Page 1 VOLUME 13, NUMBER 3, FALL …

In this note all rings are associative with identity elements and all modules are unital right
modules. Let I? be a ring and M a right R-module. Denote the socle and radical of M by Soc …

A module M is called a CS-module if every submodule of M is essential in a direct summand
of M. A ring R is called CS-semisimple if every right R-module is CS. For a ring R, we show …