Commutativity with algebraic identities involving prime ideals

Hajar El Mir; Abdellah Mamouni; Lahcen Oukhtite

doi:10.4134/CKMS.c190338

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Commun. Korean Math. Soc. 2020; 35(3): 723-731

Online first article March 10, 2020 Printed July 31, 2020

https://doi.org/10.4134/CKMS.c190338

Commutativity with algebraic identities involving prime ideals

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

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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