Let A be an alternative ring
and Aq its attached quadratic Jordan ring. We show that if A is finitely
generated by n generators then Aq is finitely generated by the monomials in A of
degree ≦ n + 1. It follows that if A is finitely generated then A is nilpotent if
and only if Aq is solvable, and for arbitrary A the Levitzki radical of A
coincides with the Levitzki radical of Aq. Finally, if A has an involution ∗
and H(A,∗) denotes the ∗-symmetric elements of A then several results
known for associative rings connecting properties of H(A,∗) to those of A
apply.
