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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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Upper bounds for GK-dimensions of finitely generated P.I. algebras
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by Allan Berele PDF
Proc. Amer. Math. Soc. 145 (2017), 1859-1864 Request permission

Abstract:

We prove that if $A$ is characteristic zero algebra generated by $k$ elements and satisfying a polynomial identity of degree $d$ then it has GK-dimension less than or equal to $k\lfloor d/2\rfloor ^2$. We conjecture that the stronger upper bound that the GK-dimension of $A$ is less than or equal to $(k-1)\lfloor d/2\rfloor ^2 +1$ and prove it in a number of special cases.
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Additional Information
  • Allan Berele
  • Affiliation: Department of Mathematics, DePaul University, Chicago, Illinois 60614
  • Email: aberele@depaul.edu
  • Received by editor(s): May 22, 2015
  • Received by editor(s) in revised form: June 21, 2016
  • Published electronically: November 21, 2016
  • Communicated by: Harm Derksen
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 1859-1864
  • MSC (2010): Primary 16P90; Secondary 16R99
  • DOI: https://doi.org/10.1090/proc/13456
  • MathSciNet review: 3611302