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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

BOUCHANNAFA, Karim; MAMOUNI, Abdellah  and  OUKHTITE, Lahcen. Structure of a quotient ring R/P and its relation with generalized derivations of R. Proyecciones (Antofagasta) [online]. 2022, vol.41, n.3, pp.623-642. ISSN 0716-0917.  http://dx.doi.org/10.22199/issn.0717-6279-4399.

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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