  Albert algebras, a specific kind of Jordan algebra, are naturally
distinguished objects among commutative non-associative algebras and also arise
naturally in the context of simple affine group schemes of type $F_4$, $E_6$,
or $E_7$. We study these objects over an arbitrary base ring $R$, with
particular attention to the case of the integers. We prove in this generality
results previously in the literature in the special case where $R$ is a field
of characteristic different from 2 and 3.
