Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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RINGS IN WHICH EVERY SEMICENTRAL IDEMPOTENT IS CENTRAL

  • Muhammad Saad (Department of Mathematics and Computer Science, Faculty of Science, Alexandria University)
  • Received : 2023.09.14
  • Accepted : 2023.10.26
  • Published : 2023.12.30
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Abstract

The RIP of rings was introduced by Kwak and Lee as a generalization of the one-sided idempotent-reflexivity property. In this study, we focus on rings in which all one-sided semicentral idempotents are central, and we refer to them as quasi-Abelian rings, extending the concept introduced by RIP. We establish that quasi-Abelianity extends to various types of rings, including polynomial rings, power series rings, Laurent series rings, matrices, and certain subrings of triangular matrix rings. Furthermore, we provide comprehensive proofs for several results that hold for RIP and are also satisfied by the quasi-Abelian property. Additionally, we investigate the structural properties of minimal non-Abelian quasi-Abelian rings.

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References

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