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On algebras with Gelfand-Kirillov dimension one

Authors: Shigeru Kobayashi and Yuji Kobayashi
Journal: Proc. Amer. Math. Soc. 119 (1993), 1095-1104
MSC: Primary 16P90; Secondary 16S15
MathSciNet review: 1158002
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Abstract: We study the growth of finitely generated algebras by means of the Ufnarovskij graph. We improve a result of Bergman about the jumps of the growth function and give a characterization of algebras with $ \operatorname{GKdim} = 1$ in terms of the Ufnarovskij graph. For monomial algebras the behavior of the growth functions is studied in more detail.

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