On Division Algebras of Degree 3 with Involution

LetDbe a division algebra of degree 3 over its centerKand letJbe an involution of the second kind onD. LetFbe the subfield ofKof elements invariant underJ, charF≠3. We present a simple proof of a theorem of A. Albert on the existence of a maximal subfield ofDwhich is Galois overFwith groupS3and prove an analog for symmetric elements of Wedderburn's Theorem on the splitting of the minimal polynomial of any element ofD. These results are then applied to the theory of the Clifford algebra of a binary cubic form.