The probability of zero multiplication in finite group algebras

Mohammed Salih, Haval M.

doi:10.22108/ijgt.2023.137640.1842

تعداد نشریات	43
تعداد شماره‌ها	1,802
تعداد مقالات	14,715
تعداد مشاهده مقاله	39,737,432
تعداد دریافت فایل اصل مقاله	15,427,086

	The probability of zero multiplication in finite group algebras
International Journal of Group Theory
مقاله 6، دوره 13، شماره 2، شهریور 2024، صفحه 189-194 اصل مقاله (456.54 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2023.137640.1842
نویسنده
Haval M. Mohammed Salih^*
Department of Mathematics, Faculty of Science, Soran University , Kawa St, Soran, Erbil, Iraq
چکیده
Let $\mathbb{F}_qG$ be a finite group algebra. We denote by $P(\mathbb{F}_qG)$ the probability that the product of two elements of $\mathbb{F}_qG$ be zero. In this paper, we obtain several results on this probability including a computing formula and characterizations. In particular, the computing formula for the $P(\mathbb{F}_qG)$ are established where $G$ is the cyclic group $C_n$, the Quaternion group $Q_8$, the symmetric group $S_3$ and $F_q$ is a finite field.
کلیدواژه‌ها
Unit؛ Zero divisor؛ Wedderburn decomposition

مراجع
[1] M. A. Esmkhani and S. M. Jafarian Amiri, The probability that the multiplication of two ring elements is zero, J. Algebra Appl., 17 (2018) 9 pp. [2] 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. [3] J. Gildea, On the order of U (Fpk D2pm ), Int. J. Pure Appl. Math., 46 (2008) 267–272. [4] 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. [5] H. M. Mohammed Salih, On the probability of zero divisor elements in group rings Int. J. Group Theory, 11 no. 4 (2022) 253–257. [6] 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. [7] H. Cheraghpour and N. G. Ghosseiri, On the idempotents, nilpotents, units and zero-divisors of finite rings. Linear Multilinear Algebra, 67 (2019) 327–336. [8] F. E. Brochero Martinez, Structure of finite dihedral group algebra, Finite Fields Appl., 35 (2015) 204-214. [9] R. Lidl and H. Niederreiter, Finite fields, Cambridge University Press, 1997. [10] S. Perlis and G. L. Walker, Abelian group algebras of finite order, Trans. Amer. Math. Soc., 68 (1950) 420–426. [11] D. David, The probability of zero multiplication in finite rings, Bull. Aust. Math. Soc., 106 (2022) 83–88.
آمار تعداد مشاهده مقاله: 230 تعداد دریافت فایل اصل مقاله: 324

سامانه مدیریت نشریات علمی. طراحی و پیاده سازی از سیناوب

پیوندهای مفید

اخبار و اعلانات

آمار

The probability of zero multiplication in finite group algebras