With a grading previously introduced by the second-named author, the
multiplication maps in the preprojective algebra satisfy a maximal rank
property that is similar to the maximal rank property proven by Hochster and
Laksov for the multiplication maps in the commutative polynomial ring. The
result follows from a more general theorem about the maximal rank property of a
minimal almost split morphism, which also yields a quadratic inequality for the
dimensions of indecomposable modules involved
