Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON COFINITELY CLOSED WEAK δ-SUPPLEMENTED MODULES

  • Received : 2019.11.18
  • Accepted : 2020.04.21
  • Published : 2020.09.25
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Abstract

A module M is called cofinitely closed weak δ-supplemented (briefly δ-ccws-module) if for any cofinite closed submodule N of M has a weak δ-supplement in M. In this paper we investigate the basic properties of δ-ccws modules. In the light of this study, we can list the main facts obtained as following: (1) Any cofinite closed direct summand of a δ-ccws module is also a δ-ccws module; (2) Let R be a left δ-V -ring. Then R is a δ-ccws module iff R is a ccws-module iff R is extending; (3) Any nonsingular homomorphic image of a δ-ccws-module is also a δ-ccws-module; (4) We characterize nonsingular δ-V -rings in which all nonsingular modules are δ-ccws.

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References

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