Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Purely Extending Modules and Their Generalizations

  • Shiv Kumar (Department of Mathematical Sciences, IIT(B. H. U.) ) ;
  • Ashok Ji Gupta (Department of Mathematical Sciences, IIT(B. H. U.) )
  • Received : 2021.06.15
  • Accepted : 2022.12.06
  • Published : 2023.03.31
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Abstract

A purely extending module is a generalization of an extending module. In this paper, we study several properties of purely extending modules and introduce the notion of purely essentially Baer modules. A module M is said to be a purely essentially Baer if the right annihilator in M of any left ideal of the endomorphism ring of M is essential in a pure submodule of M. We study some properties of purely essentially Baer modules and characterize von Neumann regular rings in terms of purely essentially Baer modules.

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Acknowledgement

We are very thankful to the referee for a thorough report and for many helpful suggestions. The first author also gratefully acknowledges financial support from UGC, INDIA to carry out this research work.

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