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On the probability of zero divisor elements in group rings | ||
International Journal of Group Theory | ||
مقاله 10، دوره 11، شماره 4، اسفند 2022، صفحه 253-257 اصل مقاله (402.74 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22108/ijgt.2021.126694.1664 | ||
نویسنده | ||
Haval M. Mohammed Salih* | ||
Department of Mathematics, Faculty of Science, Soran University , Kawa St, Soran, Erbil, Iraq | ||
چکیده | ||
Let $R$ be a non trivial finite commutative ring with identity and $G$ be a non trivial group. We denote by $P(RG)$ the probability that the product of two randomly chosen elements of a finite group ring $RG$ is zero. We show that $P(RG)<\frac{1}{4}$ if and only if $RG\ncong \mathbb{Z}_2C_2,\mathbb{Z}_3C_2, \mathbb{Z}_2C_3$. Furthermore, we give the upper bound and lower bound for $P(RG)$. In particular, we present the general formula for $P(RG)$, where $R$ is a finite field of characteristic $p$ and $|G|\leq 4$. | ||
کلیدواژهها | ||
group ring؛ probability؛ unit group؛ zero divisor | ||
مراجع | ||
[1] J. Gildea, The structure of the unit group of the group algebra F3K (C3 × D6 ), Comm. Algebra, 38 (2010) 3311–3317. | ||
آمار تعداد مشاهده مقاله: 763 تعداد دریافت فایل اصل مقاله: 248 |