Bulletin of the American Mathematical Society

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ISSN 1088-9485(e) ISSN 0273-0979(p)

A new measure of growth for countable-dimensional algebras

Author(s): John Hannah; 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.

References:

[1]: K. R. Goodearl, P. Menal, and J. Moncasi, Free and residually artinian regular rings, J. Algebra 156 (1993), 407-432. MR 1216477 (94f:16025)
[2]: G. R. Krause and T. H. Lenagan, Growth of algebras and Gelfand-Kirillov dimension, Pitman, New York, 1985. MR 781129 (86g:16001)
[3]: K. C. O'Meara, C. I. Vinsonhaler, and W. J. Wickless, Identity-preserving embeddings of countable rings into 2-generator rings, Rocky Mountain J. Math. 19 (1989), 1095-1105. MR 1039546 (91h:16057)

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