Polynomial algebras have polynomial growth

Finston, David R.

doi:10.1090/S0002-9947-1987-0876465-6

Polynomial algebras have polynomial growth
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by David R. Finston

Trans. Amer. Math. Soc. 300 (1987), 535-556

DOI: https://doi.org/10.1090/S0002-9947-1987-0876465-6

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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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