Central European Journal of Mathematics

, Volume 3, Issue 2, pp 273–281

# Generalizations of coatomic modules

• M. Tamer Koşan
• Abdullah Harmanci
Article

## Abstract

For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if, whenever N+X=M with M/X singular, we have X=M. Let ℘ be the class of all singular simple modules. Then δ(M)=Σ{ LM| L is a δ-small submodule of M} = Rejm(℘)=∩{ NM: M/N∈℘. We call M δ-coatomic module whenever NM and M/N=δ(M/N) then M/N=0. And R is called right (left) δ-coatomic ring if the right (left) R-module RR(RR) is δ-coatomic. In this note, we study δ-coatomic modules and ring. We prove M=⊕i=1n Mi is δ-coatomic if and only if each Mi (i=1,…, n) is δ-coatomic.

### Keywords

δ-small module coatomic module

### MSC (2000)

16D60 16D99 16S90

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