Associated with each
artinian ring R are two diagrams called the left and right quivers of R. We
generalize a well-known theorem on hereditary serial rings by proving that
if these quivers have no closed paths then R is a factor ring of a certain
ring of matrices over a division ring. It follows that the categories of finitely
generated left and right R-modules are Morita dual to one another. Applying our
theorem and theorems of Gabriel and Dlab and Ringel, we show how to write
explicit matrix representations of all hereditary algebras of finite module
type.
