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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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$G$-graded central polynomials and $G$-graded Posner’s theorem
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by Yakov Karasik PDF
Trans. Amer. Math. Soc. 372 (2019), 5531-5546 Request permission

Abstract:

Let $\mathbb {F}$ be a characteristic zero field, let $G$ be a residually finite group, and let $W$ be a $G$-prime and polynomial identity $\mathbb {F}$-algebra. By constructing $G$-graded central polynomials for $W$, we prove the $G$-graded version of Posner’s theorem. More precisely, if $S$ denotes all nonzero degree $e$ central elements of $W$, the algebra $S^{-1}W$ is $G$-graded simple and finite dimensional over its center.

Furthermore, we show how to use this theorem in order to recapture a result of Aljadeff and Haile stating that two $G$-simple algebras of finite dimension are isomorphix if and only if their ideals of graded identities coincide.

References
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Additional Information
  • Yakov Karasik
  • Affiliation: Department of Mathematics, Technion – Israel Institute of Technology, 32000 Haifa, Israel
  • MR Author ID: 1014910
  • Email: theyakov@gmail.com
  • Received by editor(s): February 26, 2017
  • Received by editor(s) in revised form: October 7, 2018
  • Published electronically: January 4, 2019
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 372 (2019), 5531-5546
  • MSC (2010): Primary 16R20; Secondary 16R10, 16R50
  • DOI: https://doi.org/10.1090/tran/7736
  • MathSciNet review: 4014286