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

{\small \ We generalize the concepts of \thinspace level \thinspace and \thinspace sublevel of a composition algebra to division algebras obtained by the Cayley-Dickson process. In 1967, R. B. Brown constructed, for every}$t\in $\mathbb{N}$,$anonassociativedivisionalgebra$A_{t}${\small \ of dimension}$2^t${\small \ over the power-series field}$K\{X_1,X_2,\mathrm{.}\mathrm{.}\mathrm{.},X_t\}\mathrm{.}${\small \ This gives us the possibility to construct a division algebra of \thinspace dimension}$% {\small ,2}^{t},$andprescribedlevelandsublevel$% {\small ,,2}^{k}$,$k,,t\in $\mathbb{N}$-{0} $ and dimension $2^t${\small and prescribed \thinspace level}${\small ,,2}^{k}+1$,$k\in $\mathbb{N}$% -{0},t\in $\mathbb{N}$,t\geq 2.$