Sentence:  The main tool in studying the structure of division algebras, or more generally, of central simple algebras (c.s.as) over a field \mathfrak C are the extensions of \mathfrak C that split the algebras. A field \mathfrak F\supseteq\mathfrak C is said to split a c.s.a. \mathfrak A if \mathfrak A\otimes\mathfrak F is a total matrix ring over \mathfrak F. The present study is devoted to the study of the set of all <WSD>splitting fields</WSD> of a given c.s.a. \mathfrak A. 
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".