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Minimal varieties of algebras of exponential growth
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## Minimal varieties of algebras of exponential growth

### A. Giambruno and M. Zaicev

**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.

*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

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