COFINITELY I-RAD- ⊕-SUPPLEMENTED MODULES
BURCU TAŞ
Department of Mathematics, Faculty of Sciences and Arts, Amasya University, P.O.Box 05100, Amasya, Turkey.
ERGÜL TÜRKMEN
Department of Mathematics, Faculty of Sciences and Arts, Amasya University, P.O.Box 05100, Amasya, Turkey.
BURCU NiŞANCI TÜRKMEN *
Department of Mathematics, Faculty of Sciences and Arts, Amasya University, P.O.Box 05100, Amasya, Turkey.
*Author to whom correspondence should be addressed.
Abstract
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