Commutativity with algebraic identities involving prime ideals
Commun. Korean Math. Soc. 2020 Vol. 35, No. 3, 723-731
Published online July 5, 2020
Hajar El Mir, Abdellah Mamouni, Lahcen Oukhtite
University S. M. Ben Abdellah Fez; University Moulay Isma\"{i}l; University S. M. Ben Abdellah Fez
Abstract : The purpose of this paper is to study the structure of quotient rings $R/P$ where $R$ is an arbitrary ring and $P$ is a prime ideal of $R$. Especially, we will establish a relationship between the structure of this class of rings and the behavior of derivations satisfying algebraic identities involving prime ideals. Furthermore, the characteristic of the quotient ring $R/P$ has been determined in some situations.
Keywords : Derivations, prime ideals, commutativity
MSC numbers : 16N60, 16W10, 16W25
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