Relationship between the structure of a quotient ring and the behavior of certain additive mappings
Commun. Korean Math. Soc.
Published online November 4, 2021
Karim Bouchannafa, Moulay Abdallah Idrissi, and Lahcen Oukhtite
Faculty of Sciences and Technology Fez; Polydisciplinary Faculty, Sultan Moulay Slimane University, Beni Mellal, Morocco; Faculty of Sciences and Technology Fez
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 ex-
amples 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.
MSC numbers : 16N60; 16W25; 16W10
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