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 posets I = I' boolean OR I" for which the category prin(kI) of prinjective modules over the incidence k-algebra kI of I is of finite representation type, where k is a field. In particular, it is shown that for any such poset I, 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 form q(I) associated with I. An existence of a preprojective component in prin(kI) is proved for faithful posets I which are (A) over bar-free. (C) 1998 Academic Press.