Central European Journal of Mathematics

, Volume 3, Issue 2, pp 273–281

Generalizations of coatomic modules

Authors

  • M. Tamer Koşan
    • Department of Mathematics, Faculty of Sciences and ArtsKocatepe University
  • Abdullah Harmanci
    • Department of Mathematics, Faculty of ScienceHacettepe University
Article

DOI: 10.2478/BF02479203

Cite this article as:
Koşan, M.T. & Harmanci, A. centr.eur.j.math. (2005) 3: 273. doi:10.2478/BF02479203

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} = Re jm(℘)=∩{ 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 R R(RR) is δ-coatomic. In this note, we study δ-coatomic modules and ring. We prove M=⊕ i=1 n Mi is δ-coatomic if and only if each M i (i=1,…, n) is δ-coatomic.

Keywords

δ-small module coatomic module

MSC (2000)

16D60 16D99 16S90

Copyright information

© Central European Science Journals 2005