Eine Verschärfung des Satzes von der Normalbasis. (An improvement of the normal basis theorem) (Q1085209)

The authors study some properties of the free polynomials over a field and of the free elements of an algebraic closure of a field. They also obtain several results about the decompositions of the finite abelian groups and about the completely regular elements of the Galois extensions. Their main result is the following improvement of the normal basis theorem: If L/K is a finite separable field extension then L is generated by a completely free element over K.