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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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 $ GK$dimension.


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DOI: https://doi.org/10.1090/S0002-9947-1995-1282887-9
Article copyright: © Copyright 1995 American Mathematical Society