On the probability of zero divisor elements in group rings

Mohammed Salih, Haval M.

doi:10.22108/ijgt.2021.126694.1664

تعداد نشریات	43
تعداد شماره‌ها	1,486
تعداد مقالات	12,203
تعداد مشاهده مقاله	23,237,698
تعداد دریافت فایل اصل مقاله	10,021,053

	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. [2] M. A. Esmkhani and S. M. Jafarian Amiri, The probability that the multiplication of two ring elements is zero, J. Algebra Appl., 17 (2018) pp. 9. [3] N. Makhijani, R. K. Sharma and J. B. Srivastava, The unit group of algebra of circulant matrices, Int. J. Group Theory, 3 no. 4 (2014) 13–16. [4] J. Gildea and L. Creedon, The structure of the unit group of the group algebra F 3k D6 , Int. J. Pure Appl. Math, 45, no. 2, (2008) 315-320. [5] J. Gildea, The structure of the unitary units of the group algebra F2k D8 , Int. Electron. J. Algebra, 9 (2011) 171–176. [6] J. Gildea, On the order of U (Fpk D2pm ), Int. J. Pure Appl. Math., 46 (2008) 267–272. [7] G. Tang and Y. Gao, The unit groups of F G of groups with order 12, Int. J. Pure Appl. Math., 73 (2011) 143–158. [8] M. Khan, R. K. Sharma and J. B. Srivastava, The unit group of F S4 , Acta Math. Hungar., 118 (2008) 105–113. [9] C. P. Milies and S. K. Sehgal, An introduction to group rings,Springer Science and Business Media, 1, Kluwer Academic publishers Dordrecht/Boston/London, 2002.
آمار تعداد مشاهده مقاله: 681 تعداد دریافت فایل اصل مقاله: 140

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

اخبار و اعلانات

آمار

On the probability of zero divisor elements in group rings