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Construction of a finite Dickson nearfield | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 15، دوره 14، شماره 10، دی 2023، صفحه 155-161 اصل مقاله (355.36 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.30795.4495 | ||
| نویسنده | ||
| Prudence Djagba* | ||
| Department of Mathematics, Nelson Mandela University, South Africa | ||
| تاریخ دریافت: 10 خرداد 1402، تاریخ پذیرش: 21 مرداد 1402 | ||
| چکیده | ||
| For a Dickson pair $(q,n)$ we show that $ \big \lbrace \frac{q^k-1}{q-1}, 1 \leq k \leq n \big \rbrace $ forms a finite complete set of different residues modulo $n$. We also study the construction of a finite Dickson nearfield that arises from the Dickson pair $(q,n)$. | ||
| کلیدواژهها | ||
| nearring؛ Dickson pair؛ residues | ||
| مراجع | ||
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[1] J.C. Beidleman, On near-rings and near-ring modules. PhD thesis, Pennsylvanian State University, 1966. [2] L.E. Dickson, On finite algebras, Nachr. Gesellsch. Wissensch. G¨ott. Math.-Phys. Klasse 1905 (1905), 358–393. [3] P. Djagba, Contributions to the theory of Beidleman near-vector spaces, PhD thesis, Stellenbosch University, 2019. [4] P. Djagba, On the generalized distributive set of a finite nearfield, J. Algebra 542 (2020), 130–161. [5] P. Djagba, On the center of a finite Dickson nearfield, arXiv preprint arXiv:2003.08306, 2020. [6] P. Djagba and K.-T. Howell The subspace structure of finite dimensional near-vector spaces, Linear Multilinear Algebra 68 (2020), no. 11, 2316–2336. [7] E. Ellers and H. Karzel, Endliche Inzidenzgruppen, Abhandl. Math. Seminar Hamburg 27 (1964), no. 3-4, 250–264. [8] J.D.P. Meldrum, Near Rings and Their Links with Groups, volume 134 of Research Notes in Mathematics. Pitman (Advanced Publishing Program), Boston, MA, 1985. [9] G. Pilz, Near-Rings: The Theory and its Applications, Elsevier, 2011. [10] H. Wahling, Heinz, Theorie der Fastkorper, Thales Verlag, W. Germany, 1987. [11] H. Zassenhaus, uber endliche fastk¨orper, Abhandl. Math. Seminar Univ. Hamburg 11 (1935), 187–220. | ||
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