On irreducible semigroups of matrices with traces in a subfield Original Research Article

In this paper we consider irreducible semigroups of matrices over a general field K with traces in a subfield F. Motivated by a result of Omladic–Radjabalipour–Radjavi, we prove a block matrix representation theorem for the F-algebras generated by such semigroups. We use our main results to generalize certain classical triangularization results, e.g., those due to Guralnick and Radjavi. Some other consequences of our main results are presented.