Minimal varieties of algebras of exponential growth
Authors:
A. Giambruno and M. Zaicev
Journal:
Electron. Res. Announc. Amer. Math. Soc. 6 (2000), 4044
MSC (2000):
Primary 16R10, 16P90
Published electronically:
June 6, 2000
MathSciNet review:
1767635
Fulltext PDF Free Access
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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 Tideals 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/S1079676200000780
PII:
S 10796762(00)000780
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 990100233 and 961596050.
Communicated by:
Efim Zelmanov
Article copyright:
© Copyright 2000 American Mathematical Society
