Commutativity Criteria for a Factor Ring R/P Arising from P-Centralizers

Lahcen Oukhtite*; Karim Bouchannafa; My Abdallah Idrissi

doi:10.5666/KMJ.2023.63.4.551

Article

Kyungpook Mathematical Journal 2023; 63(4): 551-560

Published online December 31, 2023

Commutativity Criteria for a Factor Ring R/P Arising from P-Centralizers

Lahcen Oukhtite* and Karim Bouchannafa, My Abdallah Idrissi

Department of Mathematics, Faculty of Sciences and Technology, S. M. Ben Abdellah University, Fez, Morocco
e-mail : oukhtitel@hotmail.com and bouchannafa.k@gmail.com

Department of Mathematics and informatics, Polydisciplinary Faculty, Box 592, Sultan Moulay Slimane University, Beni Mellal, Morocco
e-mail : myabdallahidrissi@gmail.com

Received: September 5, 2022; Revised: March 15, 2023; Accepted: March 21, 2023

Abstract

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Abstract

In this paper we consider a more general class of centralizers called I-centralizers. More precisely, given a prime ideal P of an arbitrary ring R we establish a connection between certain algebraic identities involving a pair of P-left centralizers and the structure of the factor ring R/P.

Keywords: Prime ring, Prime ideal, P-centralizer, Commutativity