Cohn-Leavitt Path Algebras and the Invariant Basis Number Property

Abstract: We give the necessary and sufficient condition for a separated Cohn-Leavitt path algebra of a finite digraph to have IBN. As a consequence, separated Cohn path algebras have IBN. We determine the non-stable K-theory of a corner ring in terms of the non-stable K-theory of the ambient ring. We give a necessary condition for a corner algebra of a separated Cohn-Leavitt path algebra of a finite graph to have IBN. We provide Morita equivalent rings which are non-IBN, but are of different types.