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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.

Copyright 2000 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 06 (2000), pp. 40-44
• Publisher Identifier: S 1079-6762(00)00078-0
• 2000 Mathematics Subject Classification. Primary 16R10, 16P90
• Key words and phrases. Varieties of algebras, polynomial identities
• Received by the editors October 4, 1999
• Posted on June 6, 2000
• Communicated by Efim Zelmanov
• Comments (When Available)

A. Giambruno

Dipartimento di Matematica ed Applicazioni, Università di Palermo, 90123 Palermo, Italy

E-mail address: a.giambruno@unipa.it

M. Zaicev

Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow 119899, Russia

E-mail address: zaicev@mech.math.msu.su

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