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Semifields from skew polynomial rings

Michel Lavrauw UGent and John Sheekey (2013) ADVANCES IN GEOMETRY. 13(4). p.583-604
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].
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
NONCOMMUTATIVE POLYNOMIALS, IRREDUCIBLE SEMILINEAR TRANSFORMATIONS, ALGEBRAS
journal title
ADVANCES IN GEOMETRY
Adv. Geom.
volume
13
issue
4
pages
583 - 604
Web of Science type
Article
Web of Science id
000325247300002
JCR category
MATHEMATICS
JCR impact factor
0.314 (2013)
JCR rank
267/302 (2013)
JCR quartile
4 (2013)
ISSN
1615-715X
DOI
10.1515/advgeom-2013-0003
language
English
UGent publication?
no
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
2152897
handle
http://hdl.handle.net/1854/LU-2152897
date created
2012-06-14 10:18:16
date last changed
2015-04-03 13:31:34
@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},
  keyword      = {NONCOMMUTATIVE POLYNOMIALS,IRREDUCIBLE SEMILINEAR TRANSFORMATIONS,ALGEBRAS},
  language     = {eng},
  number       = {4},
  pages        = {583--604},
  title        = {Semifields from skew polynomial rings},
  url          = {http://dx.doi.org/10.1515/advgeom-2013-0003},
  volume       = {13},
  year         = {2013},
}

Chicago
Lavrauw, Michel, and John Sheekey. 2013. “Semifields from Skew Polynomial Rings.” Advances in Geometry 13 (4): 583–604.
APA
Lavrauw, M., & Sheekey, J. (2013). Semifields from skew polynomial rings. ADVANCES IN GEOMETRY, 13(4), 583–604.
Vancouver
1.
Lavrauw M, Sheekey J. Semifields from skew polynomial rings. ADVANCES IN GEOMETRY. 2013;13(4):583–604.
MLA
Lavrauw, Michel, and John Sheekey. “Semifields from Skew Polynomial Rings.” ADVANCES IN GEOMETRY 13.4 (2013): 583–604. Print.