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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
DOI: https://doi.org/10.1090/S0002-9947-1985-0797061-3
MathSciNet review: 797061
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0797061-3
Article copyright: © Copyright 1985 American Mathematical Society

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