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ISSN 1079-6762

 

Minimal varieties of algebras of exponential growth


Authors: A. Giambruno and M. Zaicev
Journal: Electron. Res. Announc. Amer. Math. Soc. 6 (2000), 40-44
MSC (2000): Primary 16R10, 16P90
Published electronically: June 6, 2000
MathSciNet review: 1767635
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Abstract:

The exponent of a variety of algebras over a field of characteristic zero has been recently proved to be an integer. Through this scale we can now classify all minimal varieties of a given exponent and of finite basic rank. As a consequence we describe the corresponding T-ideals of the free algebra, and we compute the asymptotics of the related codimension sequences. We then verify in this setting some known conjectures.


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Additional Information

A. Giambruno
Affiliation: Dipartimento di Matematica ed Applicazioni, Università di Palermo, 90123 Palermo, Italy
Email: a.giambruno@unipa.it

M. Zaicev
Affiliation: Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow 119899, Russia
Email: zaicev@mech.math.msu.su

DOI: http://dx.doi.org/10.1090/S1079-6762-00-00078-0
PII: S 1079-6762(00)00078-0
Keywords: Varieties of algebras, polynomial identities
Received by editor(s): October 4, 1999
Published electronically: June 6, 2000
Additional Notes: The first author was partially supported by MURST of Italy; the second author was partially supported by the RFBR grants 99-01-00233 and 96-15-96050.
Communicated by: Efim Zelmanov
Article copyright: © Copyright 2000 American Mathematical Society