Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 17A99

Retrieve articles in all journals with MSC: 17A99

Additional Information

Article copyright: © Copyright 1987 American Mathematical Society