  We show that every central simple algebra A over a field k is Brauer
equivalent to a quotient of a finite dimensional Hopf algebra over the same
field (that is- A is Hopf Schur). If the characteristic of the field is zero,
or if the algebra has a Galois splitting field of degree prime to the
characteristic of k, we can take this Hopf algebra to be semisimple. We also
show that if F is any finite extension of k, then F is a quotient of a finite
dimensional Hopf algebra over k. We use it in order to show why the algebric
closeness assumption is necessary in a weak form of Kaplansky's tenth
conjecture, due to Stefan
