The theorem states that a simple ring R that is Artinian is isomorphic with the *n*x*n* matrix ring over a division ring D, for some integer *n*. In that case the center of D must be a field K. Therefore R is a K-algebra, and itself has K as center: R is a central simple algebra over K.

When K is the real number field **R**, possible examples are the *n*x*n* matrix rings over **R**, the complex numbers **C**, and the quaternion ring **H** only. When K is **C**, just *n*x*n* complex matrices.