Applications of two-sided α-generalized derivations to 3-prime near rings

ABSTRACT

Let N be a zero symmetric 3-prime right near ring and α:N→N be an endomorphism. In this paper, the notions of two-sided α-(generalized) derivations on N are studied. Some results characterize commutativity of 3-prime near rings are obtained. Examples proving the necessity of the 3-primeness hypothesis are given. When α = id_N, one can easily obtain the main results of [5].

KEYWORDS:

• 3-Prime near-rings
• commutativity
• two-sided α-derivations
• two-sided α-generalized derivations

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16N60
• 16W25
• 16Y30

Acknowledgments

The author would like to thank the anonymous referee for critically reading the manuscript and also for his constructive comments which substantially improved the manuscript.