2005/12/30 by Steven Diaz, Diaz, Steven P., Mark Kleiner +1
Mathematics · #13D02 #16G30 #16G70 (Primary) #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.math/0512661
openalex publication_date 2005/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.