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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Polynomial algebras have polynomial growth


Author: David R. Finston
Journal: Trans. Amer. Math. Soc. 300 (1987), 535-556
MSC: Primary 17A99
MathSciNet review: 876465
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Abstract: The definitions and basic properties of Gelfand-Kirillov dimension are extended to algebras over a field which are not necessarily associative. The results are applied to the algebra of polynomial functions on an arbitrary finite dimensional algebra to obtain polynomial growth (i.e. integral G-K dimension) for these algebras. The G-K dimension of the polynomial algebra in one indeterminate is shown to be constant on the category of all finite dimensional nomial extensions of an associative algebra.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0876465-6
PII: S 0002-9947(1987)0876465-6
Article copyright: © Copyright 1987 American Mathematical Society