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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

A new measure of growth for countable-dimensional algebras


Authors: John Hannah and K. C. O’Meara
Journal: Bull. Amer. Math. Soc. 29 (1993), 223-227
MSC (2000): Primary 16P90; Secondary 15A30, 16G99, 16S50
MathSciNet review: 1215312
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0273-0979-1993-00427-0
PII: S 0273-0979(1993)00427-0
Article copyright: © Copyright 1993 American Mathematical Society