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

Authors:
John Hannah and K. C. O’Meara

Journal:
Trans. Amer. Math. Soc. **347** (1995), 111-136

MSC:
Primary 16P90; Secondary 16E50, 16S15, 16S50

DOI:
https://doi.org/10.1090/S0002-9947-1995-1282887-9

MathSciNet review:
1282887

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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 dimension.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1995-1282887-9

Article copyright:
© Copyright 1995
American Mathematical Society