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Minimal varieties of algebras of exponential growth
Author(s):
A.
Giambruno;
M.
Zaicev
Journal:
Electron. Res. Announc. Amer. Math. Soc.
6
(2000),
40-44.
MSC (2000):
Primary 16R10, 16P90
Posted:
June 6, 2000
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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:
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
Posted:
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
Copyright of article:
Copyright
2000,
American Mathematical Society
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