Identities in $3$-prime near-rings with left multipliers

	Identities in $3$-prime near-rings with left multipliers
Journal of Algebra and Related Topics
مقاله 6، دوره 6، شماره 1، شهریور 2018، صفحه 67-77 اصل مقاله (263.86 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22124/jart.2018.10093.1096
نویسندگان
M. Ashraf^* ¹؛ A. Boua²
¹Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India
²Department of Mathematics, Physics and Computer Science, Sidi Mohammed Ben Abdellah University,Taza, Morocco
چکیده
Let $\mathcal{N}$ be a $3$-prime near-ring with the center $Z(\mathcal{N})$ and $n \geq 1$ be a fixed positive integer. In the present paper it is shown that a $3$-prime near-ring $\mathcal{N}$ is a commutative ring if and only if it admits a left multiplier $\mathcal{F}$ satisfying any one of the following properties: $(i)\:\mathcal{F}^{n}([x, y])\in Z(\mathcal{N})$, $(ii)\:\mathcal{F}^{n}(x\circ y)\in Z(\mathcal{N})$, $(iii)\:\mathcal{F}^{n}([x, y])\pm(x\circ y)\in Z(\mathcal{N})$ and $(iv)\:\mathcal{F}^{n}([x, y])\pm x\circ y\in Z(\mathcal{N})$, for all $x, y\in\mathcal{N}$.
کلیدواژه‌ها
$3$-Prime near-ring؛ derivations؛ commutativity؛ left multiplier

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