A new measure of growth for countable-dimensional algebras
John Hannah, K. C. O'Meara
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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