On Monomial Algebras of Finite Global Dimension

Abstract

Let G be an associative monomial k-algebra. If G is assumed to be finitely presented, then either G contains a free subalgebra on two monomials or else G has polynomial growth. If instead G is assumed to have finite global dimension, then either G contains a free subalgebra or else G has a finite presentation and polynomial growth. Also, a graded Hopf algebra with generators in degree one and relations in degree two contains a free Hopf subalgebra if the number of relations is small enough.

Cite this paper

@inproceedings{Anick2010OnMA, title={On Monomial Algebras of Finite Global Dimension}, author={David J Anick}, year={2010} }