#### Document Type

Article

#### Date

12-30-2005

#### Embargo Period

11-14-2011

#### Disciplines

Mathematics

#### Description/Abstract

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.

#### Recommended Citation

Diaz, Steven P. and Kleiner, Mark, "Almost Split Morphisms, Preprojective Algebras and Multiplication Maps of Maximal Rank" (2005). *Mathematics Faculty Scholarship.* Paper 75.

http://surface.syr.edu/mat/75

#### Source

Harvested from arXiv.org

## Additional Information

This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/math/0512661