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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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Polynomial identities with involution, superinvolutions and the Grassmann envelope
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by Eli Aljadeff, Antonio Giambruno and Yakov Karasik PDF
Proc. Amer. Math. Soc. 145 (2017), 1843-1857 Request permission

Abstract:

Let $A$ be an algebra with involution $*$ over a field of characteristic zero. We prove that in case $A$ satisfies a non-trivial $*$-identity, then $A$ has the same $*$-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution. As a consequence we give a positive answer to the Specht problem for algebras with involution, i.e., any T-ideal of identities of an algebra with involution is finitely generated as a T-ideal.
References
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Additional Information
  • Eli Aljadeff
  • Affiliation: Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel
  • MR Author ID: 229998
  • Email: aljadeff@tx.technion.ac.il
  • Antonio Giambruno
  • Affiliation: Dipartimento di Matematica e Informatica, Università di Palermo, Via Archirafi 34, 90123 Palermo, Italy
  • MR Author ID: 73185
  • ORCID: 0000-0002-3422-2539
  • Email: antonio.giambruno@unipa.it
  • Yakov Karasik
  • Affiliation: Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel
  • Email: yaakov@tx.technion.ac.il
  • Received by editor(s): June 12, 2016
  • Published electronically: January 11, 2017
  • Additional Notes: The first author was partially supported by the ISRAEL SCIENCE FOUNDATION(grant No. 1017/12). The second author was partially supported by GNSAGA of INDAM
  • Communicated by: Jerzy Weyman
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 1843-1857
  • MSC (2010): Primary 16R10, 16R50; Secondary 16W10
  • DOI: https://doi.org/10.1090/proc/13546
  • MathSciNet review: 3611301