ON DIVISION-ALGEBRAS OF DEGREE-3 WITH INVOLUTION

Let D be a division algebra of degree 3 over its center K and let J be an involution of the second kind on D. Let F be the subfield of K of elements invariant under J, char F not equal 3. We present a simple pr oof of a theorem of A. Albert on the existence of a maximal subfield o f D which is Galois over F with group S-3 and prove an analog for symm etric elements of Wedderburn's Theorem on the splitting of the minimal polynomial of any element of D, These results are then applied to the theory of the Clifford algebra of a binary cubic form. (C) 1996 Acade mic Press, Inc.