Artin--Wedderburn theorem

Let \(R\) be a nonzero unital ring that is semisimple as a left module over itself. Then there are integers \(m\geq 1\) and \(n_1,\ldots,n_m\geq 1\) and division rings \(D_1,\ldots,D_m\) such that \[ R \cong \bigoplus_{i=1}^m \Mat_{n_i}(D_i), \] a finite direct sum of the rings of \(n_i\times n_i\) matrices over \(D_i\).