We call a field "E" a "splitting field" for "A" over "K" if "A"⊗"E" is isomorphic to a matrix ring over "E". Every finite dimensional CSA has a splitting field: indeed, in the case when "A" is a division algebra, then a maximal subfield of "A" is a splitting field. In general by theorems of Wedderburn and Koethe there is a splitting field which is a separable extension of "K" of degree equal to the index of "A", and this splitting field is isomorphic to a subfield of "A". As an example, the field C splits the quaternion algebra H over R with