On preprojective short exact sequences in the Kronecker case

Let P,P′ be preprojective Kronecker modules (i.e., all their indecomposable components are preprojective). We give a numerical criterion in terms of the so-called Kronecker invariants for the existence of an epimorphism g:P→P′. As an application, we describe the possible middle terms in certain preprojective short exact sequences. We also prove that the possible middle terms in preprojective short exact sequences do not depend on the base field k. All the results above can be dualized for preinjective modules.