Semisimple Artinian (2,n)-rings (Q1063668)

The author proves that a semi-simple (1)-Artinian (2,n)-ring is a finite direct sum of simple (1)-Artinian (2,n)-rings. If R is a simple, (1)- Artinian, (1)-primitive (2,n)-ring then \(R\cong \Delta^ n_ m\) for some division ring \(\Delta\). Conversely, every (2,n)-ring \(\Delta^ n_ m\) is a simple (1)-Artinian, (1)-primitive (2,n)-ring. If R is a simple, (1)-Artinian (2,n)-ring which is not (1)-primitive; then there exist division rings \(k_ 1,...,k_ s\subseteq D_ m\), not necessarily subrings in \(D_ m\), such that \[ R\cong k_ 1(p_ 1,q_ 1)\oplus k_ 2(p_ 2,q_ 2)\oplus...\oplus k_ s(p_ s,q_ s). \] Conversely, any such (2,n)-ring is a simple, (1)-Artinian, non-(1)- primitive (2,n)-ring. This is a generalization of Wedderburn's theorem on the structure of semi-simple (1)-Artinian (2,n)-rings.