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ON A GENERALIZATION OF ⊕-CO-COATOMICALLY SUPPLEMENTED MODULES
Figen Eryilmaz,Esra Ozturk Sozen 호남수학회 2023 호남수학학술지 Vol.45 No.1
In this paper, we define ⊕δ-co-coatomically supplemented and co-coatomically δ-semiperfect modules as a strongly notion of ⊕- co-coatomically supplemented and co-coatomically semiperfect modules with the help of Zhou’s radical. We say that a module A is ⊕δ-cocoatomically supplemented if each co-coatomic submodule of A has a δ−supplement in A which is a direct summand of A. And a module A is co-coatomically δ-semiperfect if each coatomic factor module of A has a projective δ-cover. Also we define co-coatomically amply δ-supplemented modules and we examined the basic properties of these modules. Furthermore, we give a ring characterization for our modules. In particular, a ring R is δ-semiperfect if and only if each free R-module is co-coatomically δ-semiperfect.
F<sub>δ</sub>-SUPPLEMENTED MODULES
Turkmen, Burcu Nisanci,Eryilmaz, Figen The Honam Mathematical Society 2020 호남수학학술지 Vol.42 No.2
In this article, we define a (an amply) F<sub>δ</sub>-supplemented module in category of R-Mod. The general properties of F<sub>δ</sub>-supplemented modules are briefly discussed. Then, concentrating on the F<sub>δ</sub>-small submodule, we find the necessary and sufficient condition for F<sub>δ</sub>- supplemented modules. Also, we introduce ascending chain condition for F<sub>δ</sub>-small submodules of any module and establish a basic theorem for amply F<sub>δ</sub>-supplemented modules by using π-projectivity.