Auslander-reiten quivers of schurian orders

Abstract

We shall consider orders ⋀ over a complete discrete rank one valuation ring R in a split full matrix ring containing a complete sex of primitive orthogonal idempot ents. In case s of finite lattice type and R is the power series ring in one variable over its residexe class field k , we give a description of its index composable lattices and its Auslander-Reiten quiver in terms of representations of partially ordered sets. By a model theoretic argument, this implies a description of all indecomposable lattices if R is the completion of the ring of integers in an algebraic number field at all but possibly a finite number of primes.