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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 | ||
آمار تعداد مشاهده مقاله: 741 تعداد دریافت فایل اصل مقاله: 1,073 |