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

作者：Flaut Cristina^*

来源：Annali di Matematica Pura ed Applicata, 2013, 192(6): 1099-1114.

DOI：10.1007/s10231-012-0260-3

• Cayley-Dickson process
• Division algebra
• Level and sublevel of an algebra

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 is an element of N - {0}.

• 出版日期2013-12