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Quaternion quadratic equations in characteristic 2

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Chapman, Adam [UCL]

In this paper, we present a solution for any standard quaternion quadratic equation, i.e. an equation of the form z2 + μz + ν = 0 where μ and ν belong to some quaternion division algebra Q over some field F, assuming the characteristic of F is 2.

Document type Article de périodique (Journal article) – Article de recherche
Publication date 2015
Language Anglais
Journal information "Journal of Algebra and its Applications" - Vol. 14, no.3, p. 1-8 (2015)
Peer reviewed yes
Publisher World Scientific Publishing Co. Pte. Ltd. (Singapore)
issn 0219-4988
e-issn 1793-6829
Publication status Publié
Affiliation UCL - SST/ICTM - Institute of Information and Communication Technologies, Electronics and Applied Mathematics
Keywords Field of characteristic 2 ; Quadratic equation ; Quaternion algebra
Links
  1. ABRATE MARCO, QUADRATIC FORMULAS FOR GENERALIZED QUATERNIONS, 10.1142/s0219498809003308
  2. Albert A. A., Structure of Algebras (1961)
  3. Herstein I. N., Conjugates in division rings, 10.1090/s0002-9939-1956-0082483-6
  4. Huang Liping, So Wasin, Quadratic formulas for quaternions, 10.1016/s0893-9659(02)80003-9
  5. Maclagan-Wedderburn J. H., A theorem on finite algebras, 10.1090/s0002-9947-1905-1500717-7
  6. Scharlau Winfried, Quadratic and Hermitian Forms, ISBN:9783642699733, 10.1007/978-3-642-69971-9
  7. Wood R. M. W., Quaternionic Eigenvalues, 10.1112/blms/17.2.137
Bibliographic reference Chapman, Adam. Quaternion quadratic equations in characteristic 2. In: Journal of Algebra and its Applications, Vol. 14, no.3, p. 1-8 (2015)
Permanent URL http://hdl.handle.net/2078.1/173366