Relationship between the structure of a quotient ring and the behavior of certain additive mappings
Commun. Korean Math. Soc. 2022 Vol. 37, No. 2, 359-370 https://doi.org/10.4134/CKMS.c210126 Published online March 29, 2022 Printed April 30, 2022
Karim Bouchannafa, Moulay Abdallah Idrissi, Lahcen Oukhtite Sidi Mohamed Ben Abdellah University; Sultan Moulay Slimane University; Sidi Mohamed Ben Abdellah University
Abstract : The principal aim of this paper is to study the connection between the structure of a quotient ring $R/P$ and the behavior of special additive mappings of $R.$ More precisely, we characterize the commutativity of $R/P$ using derivations (generalized derivations) of $R$ satisfying algebraic identities involving the prime ideal $P.$ Furthermore, we provide examples to show that the various restrictions imposed in the hypothesis of our theorems are not superfluous.
Keywords : Quotient ring, prime ideal, derivations, generalized derivations, commutativity
