 The similarity classes formula_235 with the multiplication formula_236 form an abelian group called the Brauer group of "k" and is denoted by formula_237.By the Artin–Wedderburn theorem, a central simple algebra is the matrix ring of a division ring; thus, each similarity class is represented by a unique division ring.For example, formula_237 is trivial if "k" is a finite field or an algebraically closed field (more generally quasi-algebraically closed field; cf.