On permuting $n$-derivations in near-rings
Commun. Korean Math. Soc. 2013 Vol. 28, No. 4, 697-707
https://doi.org/10.4134/CKMS.2013.28.4.697
Printed October 1, 2013
Mohammad Ashraf and Mohammad Aslam Siddeeque
Aligarh Muslim University, Aligarh Muslim University
Abstract : In this paper, we introduce the notion of permuting $n$-deri\-vations in near-ring $N$ and investigate commutativity of addition and multiplication of $N$. Further, under certain constrants on a $n!$-torsion free prime near-ring $N$, it is shown that a permuting $n$-additive mapping $D$ on $N$ is zero if the trace $d$ of $D$ is zero. Finally, some more related results are also obtained.
Keywords : left near-rings, zero symmetric, derivations, permuting $n$-derivations
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