On the probability of zero divisor elements in group rings

Mohammed Salih, Haval M.

doi:10.22108/ijgt.2021.126694.1664

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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
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On the probability of zero divisor elements in group rings