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Annali di Matematica Pura ed Applicata

, Volume 192, Issue 6, pp 1099–1114 | Cite as

Levels and sublevels of algebras obtained by the Cayley–Dickson process

  • Cristina Flaut
Article

Abstract

In this paper, we generalize the concepts of level and sublevel of a composition algebra to algebras obtained by the Cayley–Dickson process and we will show that, in the case of level for algebras obtained by the Cayley–Dickson process, the situation is the same as for the integral domains, proving that for any positive integer n, there is an algebra A obtained by the Cayley–Dickson process with the norm form anisotropic over a suitable field, which has the level \({n \in \mathbb{N}-\{0\}}\) .

Keywords

Cayley–Dickson process Division algebra Level and sublevel of an algebra 

Mathematics Subject Classification (2000)

17A35 17A20 17A75 17A45 

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag 2012

Authors and Affiliations

  1. 1.“Ovidius” University of ConstanţaConstanţaRomânia

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