Asian Journal of Mathematics and Computer Research
 

Asian Journal of Mathematics and Computer Research, ISSN No. : 2395-4205 (Print), 2395-4213 (Online), Vol.: 22, Issue.: 1

Original Research Article

COFINITELY I-RAD- ⊕-SUPPLEMENTED MODULES

 

BURCU TAŞ1, ERGÜL TÜRKMEN1 AND BURCU NiŞANCI TÜRKMEN1*
1Department of Mathematics, Faculty of Sciences and Arts, Amasya University, P.O.Box 05100, Amasya, Turkey.

Abstracts

Let M be an R-module and let I be an ideal of R. We say that M is cofinitely I-Rad- ⊕-supplemented modules, provided for every cofinite submodule N of M, there exists a direct summand K of M such that M = N + K, N ∩ K ⊆ IK and N ∩ K ⊆ Rad(K). The aim of this paper is to show new properties of cofinitely I-Rad- ⊕-supplemented modules. We show that cofinitely I-Rad- ⊕- supplemented modules is closed under finite direct sums. In addition, we prove that an R-module M is cofinitely I-Rad- ⊕-supplemented if and only if K and M/K are cofinitely I-Rad- ⊕-supplemented for an ideal I of R and cofinite fully invariant direct summand K of M.

Keywords :

cgs-module; cofinitely Rad- ⊕-supplemented module; cofinitely I-Rad- ⊕-supplemented module.