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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, UniversitΓ  di Palermo, 90123 Palermo, Italy
MR Author ID: 73185
ORCID: 0000-0002-3422-2539

M. Zaicev
Affiliation: Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow 119899, Russia
MR Author ID: 256798

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