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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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Group algebras whose units satisfy a group identity
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by Antonio Giambruno, Sudarshan Sehgal and Angela Valenti PDF
Proc. Amer. Math. Soc. 125 (1997), 629-634 Request permission

Abstract:

Let $FG$ be the group algebra of a torsion group over an infinite field $F$. Let $U$ be the group of units of $FG$. We prove that if $U$ satisfies a group identity, then $FG$ satisfies a polynomial identity. This confirms a conjecture of Brian Hartley.
References
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Additional Information
  • Antonio Giambruno
  • Affiliation: Dipartimento di Matematica, Universitá di Palermo, via Archirafi 34, 90123 Palermo, Italy
  • MR Author ID: 73185
  • ORCID: 0000-0002-3422-2539
  • Email: giambruno@ipamat.math.unipa.it, avalenti@ipamat.math.unipa.it
  • Sudarshan Sehgal
  • Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
  • MR Author ID: 158130
  • Email: ssehgal@schur.math.ualberta.ca
  • Angela Valenti
  • Affiliation: Dipartimento di Matematica, Universitá di Palermo, via Archirafi 34, 90123 Palermo, Italy
  • Received by editor(s): June 26, 1995
  • Additional Notes: Research supported by NR and MURST of Italy and NSERC of Canada.
  • Communicated by: Ronald M. Solomon
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 629-634
  • MSC (1991): Primary 16S34; Secondary 20C05
  • DOI: https://doi.org/10.1090/S0002-9939-97-03581-8
  • MathSciNet review: 1350944