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Semifields from skew polynomial rings
-
Michel Lavrauw
and
John Sheekey
Published/Copyright:
October 1, 2013
Abstract
Skew polynomial rings are used to construct finite semifields, following from a construction of Ore and Jacobson of associative division algebras. Johnson and Jha [10] constructed the so-called cyclic semifields, obtained using irreducible semilinear transformations. In this work we show that these two constructions in fact lead to isotopic semifields, show how the skew polynomial construction can be used to calculate the nuclei more easily, and provide an upper bound for the number of isotopism classes, improving the bounds obtained by Kantor and Liebler in [13] and implicitly by Dempwolff in [2].
Published Online: 2013-10-01
Published in Print: 2013-10
© 2013 by Walter de Gruyter GmbH & Co.
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Articles in the same Issue
- Masthead
- Some remarks on Nijenhuis brackets, formality, and Kähler manifolds
- Semifields from skew polynomial rings
- A note on CR quaternionic maps
- On maximal curves of Fermat type
- On the singular locus of sets definable in a quasianalytic structure
- A product integral representation of mixed volumes of two convex bodies
- The Tutte polynomial of the Sierpiński and Hanoi graphs
- A lower bound for the Ricci curvature of submanifolds in generalized Sasakian space forms
- The canonical contact structure on the space of oriented null geodesics of pseudospheres and products
- Inscribable stacked polytopes
- Differential Harnack estimates for backward heat equations with potentials under an extended Ricci flow
