Sentence:  Group algebras are defined over the prime field \Q or \mathbb F_p (depending on the characteristic), and by what we have just proved \Q G and \mathbb F_p G have <WSD>splitting fields</WSD> that are finite degree extensions of the prime field.... / Some other basic facts about <WSD>splitting fields</WSD> are left to the exercises at the end of this chapter. Thus, if A is a finite-dimensional algebra over a field F that is a <WSD>splitting field</WSD> for A and E \supset F is a field extension, it is the case that every simple E\otimes_F A-module can be written in F (Exercises 4 and 8). 
Meaning of the word marked with <WSD> tags:  Given a finite-dimensional "K"-algebra (algebra over a field), an extension field whose every simple (indecomposable) module is absolutely simple (remains simple after the scalar field has been extended to said extension field).