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ON A GENERALIZATION OF ⊕-CO-COATOMICALLY SUPPLEMENTED MODULES
ESRA OZTURK SOZEN,FIGEN ERYILMAZ 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.
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