identities on associative algebras
Authors:
Y. Bahturin, A. Giambruno and M. Zaicev
Journal:
Proc. Amer. Math. Soc. 127 (1999), 6369
MSC (1991):
Primary 16R50; Secondary 16W20
MathSciNet review:
1468180
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Abstract 
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Abstract: Let be an algebra over a field and a finite group of automorphisms and antiautomorphisms of . We prove that if satisfies an essential polynomial identity of degree , then the codimensions of are exponentially bounded and satisfies a polynomial identity whose degree is bounded by an explicit function of . As a consequence we show that if is an algebra with involution satisfying a polynomial identity of degree , then the codimensions of are exponentially bounded; this gives a new proof of a theorem of Amitsur stating that in this case must satisfy a polynomial identity and we can now give an upper bound on the degree of this identity.
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Additional Information
Y. Bahturin
Affiliation:
$\mathrm{(Y. Bahturin and M. Zaicev)}$ Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119899 Russia
Email:
bahturin@mech.math.msu.su
A. Giambruno
Affiliation:
$\mathrm{(A. Giambruno)}$ Dipartimento di Matematica e Applicazioni, Università di Palermo, Via Archirafi 34, 90123 Palermo, Italy
Email:
a.giambruno@unipa.it
M. Zaicev
Email:
zaicev@nw.math.msu.su
DOI:
http://dx.doi.org/10.1090/S000299399904530X
PII:
S 00029939(99)04530X
Received by editor(s):
December 18, 1996
Received by editor(s) in revised form:
May 13, 1997
Additional Notes:
Y. Bahturin and M. Zaicev acknowledge support by the Russian Foundation of Fundamental Research, grant 960100146. A. Giambruno was supported by MURST and CNR of Italy.
Communicated by:
Ken Goodearl
Article copyright:
© Copyright 1999
American Mathematical Society
