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Polynomial growth of the codimensions: a characterization
Author(s):
A.
Giambruno;
S.
Mishchenko
Journal:
Proc. Amer. Math. Soc.
138
(2010),
853-859.
MSC (2010):
Primary 17A50, 16R10, 16P90;
Secondary 20C30
Posted:
November 10, 2009
MathSciNet review:
2566551
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References |
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Additional information
Abstract:
Let  be a not necessarily associative algebra over a field of characteristic zero. Here we characterize the T-ideal of identities of  in case the corresponding sequence of codimensions is polynomially bounded.
References:
-
- 1.
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- 2.
- V. Drensky, ``Free Algebras and PI-Algebras, Graduate Course in Algebra'', Springer-Verlag Singapore, Singapore, 2000. MR 1712064 (2000j:16002)
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- 4.
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- 7.
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![$ [[X\sb{1}, X\sb{2}, X\sb{3}], [X\sb{4}, X\sb{5}, X\sb{6}]]=0$](/proc/2010-138-03/S0002-9939-09-10160-0/gif-references0/img2.gif) over a field of characteristic zero (Russian), Sibirsk. Mat. Zh. 25 (1984), 3, 40-54. MR 746940 (85k:17016) - 10.
- K. A. Zhevlakov, A. M. Slin'ko, I. P. Shestakov, A. I. Shirshov, ``Rings That Are Nearly Associative'', Pure and Applied Mathematics, Vol. 104, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1982. MR 668355 (83i:17001)
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Additional Information:
A.
Giambruno
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Palermo, Via Archirafi 34, 90123 Palermo, Italy
Email:
a.giambruno@unipa.it
S.
Mishchenko
Affiliation:
Department of Algebra and Geometric Computations, Ulyanovsk State University, Ulyanovsk 432970, Russia
Email:
mishchenkosp@mail.ru
DOI:
10.1090/S0002-9939-09-10160-0
PII:
S 0002-9939(09)10160-0
Keywords:
Polynomial identity,
cocharacter,
codimension
Received by editor(s):
March 9, 2009,
Received by editor(s) in revised form:
August 6, 2009
Posted:
November 10, 2009
Additional Notes:
The first author was partially supported by MIUR of Italy
The second author was partially supported by RFBR grant 07-01-00080.
Communicated by:
Martin Lorenz
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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