It is wellknown the Hurwitz theorem showing that every unital composition algebra is of dimension 1, 2, 4 or 8 over the base field.
Is there an analogue in the non unital case? ¿Do non unital composition algebras of arbitrary dimension exist?
It is wellknown the Hurwitz theorem showing that every unital composition algebra is of dimension 1, 2, 4 or 8 over the base field. Is there an analogue in the non unital case? ¿Do non unital composition algebras of arbitrary dimension exist? 

