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A new measure of growth for countable-dimensional algebras

John Hannah·K. C. O'Meara
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Abstract

A new dimension function on countable-dimensional algebras (over a field) is described. Its dimension values for finitely generated algebras exactly fill the unit interval $[0,1]$. Since the free algebra on two generators turns out to have dimension 0 (although conceivably some Noetherian algebras might have positive dimension!), this dimension function promises to distinguish among algebras of infinite GK-dimension.

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John Hannah, K. C. O'Meara. 1993-10-01. A new measure of growth for countable-dimensional algebras. https://arxiv.org/abs/math/9310230

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