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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.41 no.3 Antofagasta June 2022 


Structure of a quotient ring R/P and its relation with generalized derivations of R

Karim Bouchannafa1 

Abdellah Mamouni2 

Lahcen Oukhtite3 

1 Department of Mathematics, Faculty of Science and Technology, Sidi Mohamed Ben Abdellah University, Box 2202, Fez, Morocco. E-mail:

2 Department of Mathematics, Faculty of Science, University Moulay Ismaïl, Meknes, Morocco. email:

3 Department of Mathematics, Faculty of Science and Technology, Sidi Mohamed Ben Abdellah University, Box 2202, Fez, Morocco


The fundamental aim of this paper is to investigate the structure of a quotient ring R/P where R is an arbitrary ring and P is a prime ideal of R. More precisely, we will characterize the commutativity of R/P via the behavior of generalized derivations of R satisfying algebraic identities involving the prime ideal P. Moreover, various wellknown results characterizing the commutativity of prime (semi-prime)rings have been extended. Furthermore, examples are given to prove that the restrictions imposed on the hypothesis of the various theorems were not superfluous.

Keywords: Quotient ring; prime ideal; generalized derivations; commutativity

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Received: August 30, 2020; Accepted: December 30, 2021

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