Relationship between the structure of a factor ring $R/P$ and derivations of $R$

Karim Bouchannafa; Moulay Abdallah Idrissi; Lahcen Oukhtite

doi:10.4134/BKMS.b220654

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2023; 60(5): 1281-1293

Online first article July 10, 2023 Printed September 30, 2023

https://doi.org/10.4134/BKMS.b220654

Relationship between the structure of a factor ring $R/P$ and derivations of $R$

Karim Bouchannafa, Moulay Abdallah Idrissi, Lahcen Oukhtite

Sidi Mohamed Ben Abdellah University-Fez; Sidi Mohamed Sultan Moulay Slimane University-Beni Mellal; Sidi Mohamed Ben Abdellah University-Fez

Abstract

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Abstract

The purpose of this paper is to study the relationship between the structure of a factor ring $R/P$ and the behavior of some derivations of $R$. More precisely, we establish a connection between the commutativity of $R/P$ and derivations of $R$ satisfying specific identities involving the prime ideal $P$. Moreover, we provide an example to show that our results cannot be extended to semi-prime ideals.

Keywords: Prime ideals, factor ring, derivations, commutativity

MSC numbers: Primary 16U80, 16W25, 16N60