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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Actions of pointed Hopf algebras with reduced pi invariants
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by Piotr Grzeszczuk and Małgorzata Hryniewicka PDF
Proc. Amer. Math. Soc. 135 (2007), 2381-2389 Request permission

Abstract:

Let $R$ be an $H$-module algebra, where $H$ is a pointed Hopf algebra acting on $R$ finitely of dimension $N$. Suppose that $L^H\neq 0$ for every nonzero $H$-stable left ideal of $R$. It is proved that if $R^H$ satisfies a polynomial identity of degree $d$, then $R$ satisfies a polynomial identity of degree $dN$ provided at least one of the following additional conditions is fulfilled:

  1. $R$ is semiprime and $R^H$ is almost central in $R$,

  2. $R$ is reduced.

If we also assume that $R^H$ is central, then $R$ satisfies the standard polynomial identity of degree $2[\sqrt {N}]$, where $[\sqrt {N}]$ is the greatest integer in $\sqrt {N}$.

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Additional Information
  • Piotr Grzeszczuk
  • Affiliation: Faculty of Computer Science, Technical University of Białystok, Wiejska 45A, 15-351 Białystok, Poland
  • Email: piotrgr@pb.bialystok.pl
  • Małgorzata Hryniewicka
  • Affiliation: Institute of Mathematics, University of Białystok, Akademicka 2, 15-267 Białystok, Poland
  • Email: margitt@math.uwb.edu.pl
  • Received by editor(s): January 8, 2006
  • Received by editor(s) in revised form: April 25, 2006
  • Published electronically: March 29, 2007
  • Additional Notes: The first author was supported by Polish KBN grant No. 1 P03A 032 27
  • Communicated by: Martin Lorenz
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 2381-2389
  • MSC (2000): Primary 16R20, 16S40, 16W30
  • DOI: https://doi.org/10.1090/S0002-9939-07-08769-2
  • MathSciNet review: 2302559