Commun. Korean Math. Soc. 2024; 39(2): 353-361
Online first article April 24, 2024 Printed April 30, 2024
https://doi.org/10.4134/CKMS.c230233
Copyright © The Korean Mathematical Society.
Abdelkarim Boua, Abderrahmane Raji, Abdelilah Zerbane
Sidi Mohammed Ben Abdellah University; Sultan Moulay Slimane University; Sidi Mohammed Ben Abdellah University
We consider $\mathcal{N}$ to be a $3$-prime field and $\mathcal{P}$ to be a prime ideal of $\mathcal{N}.$ In this paper, we study the commutativity of the quotient near-ring $\mathcal{N}/\mathcal{P}$ with left multipliers and derivations satisfying certain identities on $P$, generalizing some well-known results in the literature. Furthermore, an example is given to illustrate the necessity of our hypotheses.
Keywords: Prime near-rings, derivations, left multipliers, commutativity
MSC numbers: Primary 16N60; Secondary 16W25, 16Y30
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