Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

On monomial algebras of finite global dimension


Author: David J. Anick
Journal: Trans. Amer. Math. Soc. 291 (1985), 291-310
MSC: Primary 16A06; Secondary 16A60, 55P35
MathSciNet review: 797061
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G$ be an associative monomial $ {\mathbf{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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 16A06, 16A60, 55P35

Retrieve articles in all journals with MSC: 16A06, 16A60, 55P35


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0797061-3
PII: S 0002-9947(1985)0797061-3
Article copyright: © Copyright 1985 American Mathematical Society