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We show that every central simple algebra A over a field k is Brauerequivalent to a quotient of a finite dimensional Hopf algebra over the samefield (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 thecharacteristic of k, we can take this Hopf algebra to be semisimple. We alsoshow that if F is any finite extension of k, then F is a quotient of a finitedimensional Hopf algebra over k. We use it in order to show why the algebriccloseness assumption is necessary in a weak form of Kaplansky's tenthconjecture, due to Stefan

Every central simple algebra is Hopf Schur