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