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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Identities of graded algebras and codimension growth
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by Yu. A. Bahturin and M. V. Zaicev PDF
Trans. Amer. Math. Soc. 356 (2004), 3939-3950 Request permission

Abstract:

Let $A=\oplus _{g\in G}A_g$ be a $G$-graded associative algebra over a field of characteristic zero. In this paper we develop a conjecture that relates the exponent of the growth of polynomial identities of the identity component $A_e$ to that of the whole of $A$, in the case where the support of the grading is finite. We prove the conjecture in several natural cases, one of them being the case where $A$ is finite dimensional and $A_e$ has polynomial growth.
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Additional Information
  • Yu. A. Bahturin
  • Affiliation: Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Newfoundland, Canada A1A 5K9 – and – Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119899, Russia
  • MR Author ID: 202355
  • Email: yuri@math.mun.ca
  • M. V. Zaicev
  • Affiliation: Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119899, Russia
  • MR Author ID: 256798
  • Email: zaicev@mech.math.msu.su
  • Received by editor(s): March 6, 2002
  • Received by editor(s) in revised form: May 29, 2003
  • Published electronically: January 16, 2004
  • Additional Notes: The first author was partially supported by MUN Dean of Science Research Grant #38647
    The second author was partially supported by RFBR, grants 99-01-00233 and 00-15-96128
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 3939-3950
  • MSC (2000): Primary 16R10, 16W50
  • DOI: https://doi.org/10.1090/S0002-9947-04-03426-9
  • MathSciNet review: 2058512