Honam Mathematical Journal (호남수학학술지)

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ON A GENERALIZATION OF ⊕-CO-COATOMICALLY SUPPLEMENTED MODULES

  • FIGEN ERYILMAZ (Department of Mathematical Sciences, Faculty of Education, Ondokuz Mayis University) ;
  • ESRA OZTURK SOZEN (Department of Mathematics, Sinop University)
  • Received : 2022.09.12
  • Accepted : 2022.10.28
  • Published : 2023.03.25
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Abstract

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-co-coatomically 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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References

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