We obtain an equivalence relation on CSAs over "K" by the Artin–Wedderburn theorem (Wedderburn's part, in fact), to express any CSA as a M("n", "D") for some division algebra "D". If we look just at "D", that is, if we impose an equivalence relation identifying M("m", "D") with M("n", "D") for all positive integers "m" and "n", we get the Brauer equivalence relation on CSAs over "K". The elements of the Brauer group are the Brauer equivalence classes of CSAs over "K".