A note about algebras obtained by the Cayley-Dickson process

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$^{k}$ $k, t\in \Bbb{N}^{*}.$

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