Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2019; 34(1): 17-26

Online first article June 25, 2018      Printed January 31, 2019

https://doi.org/10.4134/CKMS.c170445

Copyright © The Korean Mathematical Society.

Structure of $3$-prime near-rings satisfying some identities

Abdelkarim Boua

Sidi Mohammed Ben Abdellah University

Abstract

In this paper, we investigate commutativity of $3$-prime near-rings $\mathcal{N}$ in which $(1, \alpha)$-derivations satisfy certain algebraic identities. Some well-known results characterizing commutativity of $3$-prime near-rings have been generalized. Furthermore, we give some examples show that the restriction imposed on the hypothesis is not superfluous.

Keywords: $3$-prime near-rings, commutativity, $(1, \alpha)$-derivations, two sided $\alpha$-derivations

MSC numbers: Primary 16N60, 16W25, 16Y30