Sentence:  Every finite dimensional central simple algebra has a <WSD>splitting field</WSD>: moreover, if said CSA is a division algebra, then a maximal subfield of it is a <WSD>splitting field</WSD>. 
Meaning of the word marked with <WSD> tags:  Given a central simple algebra "A" over a field "K", another field, "E", such that the tensor product "A"⊗"E" is isomorphic to a matrix ring over "E".