A new measure of growth for countable-dimensional algebras. I

Hannah, John; O’Meara, K. C.

doi:10.1090/S0002-9947-1995-1282887-9

A new measure of growth for countable-dimensional algebras. I
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by John Hannah and K. C. O’Meara PDF

Trans. Amer. Math. Soc. 347 (1995), 111-136 Request permission

Abstract:

A new dimension function on countable-dimensional algebras (over a field) is described. Its dimension values lie in 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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