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Semifields from skew polynomial rings

Michel Lavrauw (UGent) and John Sheekey
(2013) ADVANCES IN GEOMETRY. 13(4). p.583-604
Author
Organization
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].
Keywords
NONCOMMUTATIVE POLYNOMIALS, IRREDUCIBLE SEMILINEAR TRANSFORMATIONS, ALGEBRAS

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Citation

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MLA
Lavrauw, Michel, and John Sheekey. “Semifields from Skew Polynomial Rings.” ADVANCES IN GEOMETRY, vol. 13, no. 4, 2013, pp. 583–604, doi:10.1515/advgeom-2013-0003.
APA
Lavrauw, M., & Sheekey, J. (2013). Semifields from skew polynomial rings. ADVANCES IN GEOMETRY, 13(4), 583–604. https://doi.org/10.1515/advgeom-2013-0003
Chicago author-date
Lavrauw, Michel, and John Sheekey. 2013. “Semifields from Skew Polynomial Rings.” ADVANCES IN GEOMETRY 13 (4): 583–604. https://doi.org/10.1515/advgeom-2013-0003.
Chicago author-date (all authors)
Lavrauw, Michel, and John Sheekey. 2013. “Semifields from Skew Polynomial Rings.” ADVANCES IN GEOMETRY 13 (4): 583–604. doi:10.1515/advgeom-2013-0003.
Vancouver
1.
Lavrauw M, Sheekey J. Semifields from skew polynomial rings. ADVANCES IN GEOMETRY. 2013;13(4):583–604.
IEEE
[1]
M. Lavrauw and J. Sheekey, “Semifields from skew polynomial rings,” ADVANCES IN GEOMETRY, vol. 13, no. 4, pp. 583–604, 2013.
@article{2152897,
  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].}},
  author       = {{Lavrauw, Michel and Sheekey, John}},
  issn         = {{1615-715X}},
  journal      = {{ADVANCES IN GEOMETRY}},
  keywords     = {{NONCOMMUTATIVE POLYNOMIALS,IRREDUCIBLE SEMILINEAR TRANSFORMATIONS,ALGEBRAS}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{583--604}},
  title        = {{Semifields from skew polynomial rings}},
  url          = {{http://doi.org/10.1515/advgeom-2013-0003}},
  volume       = {{13}},
  year         = {{2013}},
}
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