Ore Extension Rings Satisfy the Weak PS-Rings

Authors

  • Mohamed Farahat Department of Mathematics and Statistics, Faculty of Science, Taif University, Taif, KSA. https://orcid.org/0000-0003-4731-7139
  • Salha Al-Bogamy Department of Mathematics and Statistics, Faculty of Science, Taif University, Taif, KSA.

DOI:

https://doi.org/10.29020/nybg.ejpam.v14i1.3886

Keywords:

PS-ring, weak PS-ring, Ore extension

Abstract

The main result of this paper is that: If R is a weak right PS-ring, then A = R[x; α, δ], the Ore extension ring, is a weak right PS-ring whenever the following conditions hold on R is an (α, δ)-compatible NI-ring with nil(R) nilpotent, α(e) = e and δ(e) = 0 for every idempotent e ∈ R.

Author Biographies

  • Mohamed Farahat, Department of Mathematics and Statistics, Faculty of Science, Taif University, Taif, KSA.

    Department of Mathematics and Statistics, Faculty of Science, Taif University, Taif, KSA.

  • Salha Al-Bogamy, Department of Mathematics and Statistics, Faculty of Science, Taif University, Taif, KSA.

    Department of Mathematics and Statistics, Faculty of Science, Taif University, Taif, KSA.

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Published

2021-01-31

Issue

Vol. 14 No. 1: (January 2021)

License

Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.

European Journal of Pure and Applied Mathematics will be Copyright Holder.

How to Cite

Ore Extension Rings Satisfy the Weak PS-Rings. (2021). European Journal of Pure and Applied Mathematics, 14(1), 164-172. https://doi.org/10.29020/nybg.ejpam.v14i1.3886