  In this paper, \thinspace \thinspace we generalize the concepts of \thinspace
level \thinspace and \thinspace sublevel of a composition algebra to algebras
obtained by the Cayley-Dickson process. In 1967, R. B. Brown constructed, for
every}$t\in \Bbb{N},${\small % \ a division algebra}$A_{t}${\small \ of
dimension}$2^{t}${\small \ over the power-series
field}$K\{X_{1},X_{2},...,X_{t}\}.\,${\small \ This gives us the possibility to
construct a division algebra of \thinspace dimension \thinspace
2}$^{t}\,${\small and prescribed \thinspace level and sublevel \thinspace
\thinspace 2}$^{k}${\small ,\thinspace \thinspace}$k,\,t\in \Bbb{%
N}^{*}${\small \ and a division algebra of \thinspace dimension \thinspace}$%
2^{t}+1,t\in \Bbb{N}\,${\small and prescribed \thinspace level and sublevel}%
$\,2^{k}+1,k\in \Bbb{N}.\,\medskip $
