Bipartite Posets of Finite Prinjective Type

One of the main results of this paper is Theorem 1.2, which contains a characterization of finite bipartite posetsI = I′ I″ for which the category prin(kI) of prinjective modules over the incidencek-algebrakIofIis of finite representation type, wherekis a field. In particular, it is shown that for any such posetI, the Auslander–Reiten quiver of the category prin(kI) has no oriented cycle, and there is a bijection between the isomorphism classes of indecomposable objects in prin(kI) and the positive roots of the quadratic formqIassociated withI. An existence of a preprojective component in prin(kI) is proved for faithful posetsIwhich are -free.