-identities on associative algebras

Authors:
Y. Bahturin, A. Giambruno and M. Zaicev

Journal:
Proc. Amer. Math. Soc. **127** (1999), 63-69

MSC (1991):
Primary 16R50; Secondary 16W20

MathSciNet review:
1468180

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be an algebra over a field and a finite group of automorphisms and anti-automorphisms 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:
https://doi.org/10.1090/S0002-9939-99-04530-X

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 96-01-00146. A. Giambruno was supported by MURST and CNR of Italy.

Communicated by:
Ken Goodearl

Article copyright:
© Copyright 1999
American Mathematical Society