For a field "k", a "k"-algebra is central if its center is "k" and is simple if it is a simple ring. Since the center of a simple "k"-algebra is a field, any simple "k"-algebra is a central simple algebra over its center. In this section, a central simple algebra is assumed to have finite dimension. Also, we mostly fix the base field; thus, an algebra refers to a "k"-algebra. The matrix ring of size "n" over a ring "R" will be denoted by formula_222.