### Description:

The main concept of this part of the paper is
that of a reduced exponent matrix and its quiver, which is strongly
connected and simply laced. We give the description of quivers of
reduced Gorenstein exponent matrices whose number s of vertices
is at most 7. For 2 6 s 6 5 we have that all adjacency matrices of
such quivers are multiples of doubly stochastic matrices. We prove
that for any permutation σ on n letters without fixed elements
there exists a reduced Gorenstein tiled order ¤ with σ(E) = σ.
We show that for any positive integer k there exists a Gorenstein
tiled order ¤k with in¤k = k. The adjacency matrix of any cyclic
Gorenstein order ¤ is a linear combination of powers of a permutation
matrix P¾ with non-negative coefficients, where σ = σ(¤).
If A is a noetherian prime semiperfect semidistributive ring of a
finite global dimension, then Q(A) be a strongly connected simply
laced quiver which has no loops.