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