Albert algebras over and other rings

Albert algebras, a specific kind of Jordan algebra, are naturally distinguished objects among commutative nonassociative algebras and also arise naturally in the context of simple affine group schemes of type F₄ , E₆ , or E₇ . We study these objects over an arbitrary base ring R , with particular attention to the case R = Z . 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.