Separable alternative algebras over commutative rings (Q1061211)

Let A be a unital alternative algebra over a commutative ring R, \(U_ R(A)\) be a unital universal multiplication envelope of A. The algebra A is called separable over R if \(U_ R(A)\) is a separable associative R- algebra. The author proves that a unital alternative R-algebra A is separable over R if and only if A is the direct sum of ideals B and C such that (i) B is a separable associative R-algebra, (ii) C is finitely spanned and projective of rank 8 over its center Z(C), (iii) C has a nondegenerate quadratic from n(x) over Z(C) such that \(n(xy)=n(x)n(y)\) for all x,y\(\in C\), (iv) Z(C) is a separable associative R-algebra.