On commutativity of alternative rings with [xy^n x±yx^n y,x]=0

Authors

  • Abubakar Salisu Department of Transport, Planning and Management, Federal polytechnic Daura Katsina State. Nigeria.
  • Shu’aibu Salisu Department of computer science federal polytechnic Daura Katsina state. Nigeria.
  • Mustapha Mannir Gafai Department of Mathematics and Statistics Umaru Musa Yar’adua University Katsina. Nigeria.

DOI:

https://doi.org/10.58496/BJM/2024/007

Keywords:

Alternative ring, anti-commutator, n!-torsion free, commutator, prime rings

Abstract

Let R be a n-torsion free with identity 1 ,In this article we investigate and prove the commutativity of alternative ring of the property(p_1 ), (p_2) and(p_3 ) under suitable constraints.

      (p_1 )       [xy^n x±yx^n y,x]=0

      (p_2 )        [xy^n x±yx^n y,y]=0    

      (p_3)     [x(〖xy)〗^2+(〖xy)〗^2 x,x] = 0.   ∀ x,y ∈R.

 

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Published

2024-05-21

How to Cite

Salisu , A., Salisu , S., & Gafai , M. M. (2024). On commutativity of alternative rings with [xy^n x±yx^n y,x]=0 . Babylonian Journal of Mathematics, 2024, 53–55. https://doi.org/10.58496/BJM/2024/007
CITATION
DOI: 10.58496/BJM/2024/007
Published: 2024-05-21

Issue

Vol. 2024 (2024)

Section

Articles