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Journal of the American Mathematical Society

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

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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The module structure of a group action on a polynomial ring: A finiteness theorem
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by Dikran B. Karagueuzian and Peter Symonds PDF
J. Amer. Math. Soc. 20 (2007), 931-967 Request permission

Abstract:

Consider a group acting on a polynomial ring over a finite field. We study the polynomial ring as a module for the group and prove a structure theorem with several striking corollaries. For example, any indecomposable module that appears as a summand must also appear in low degree, and so the number of isomorphism types of such summands is finite. There are also applications to invariant theory, giving a priori bounds on the degrees of the generators.
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Additional Information
  • Dikran B. Karagueuzian
  • Affiliation: Mathematics Department, Binghamton University, P.O. Box 6000, Binghamton, New York 13902-6000
  • Email: dikran@math.binghamton.edu
  • Peter Symonds
  • Affiliation: School of Mathematics, University of Manchester, P.O. Box 88, Manchester M60 1QD, United Kingdom
  • Email: Peter.Symonds@manchester.ac.uk
  • Received by editor(s): March 17, 2005
  • Published electronically: April 11, 2007
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 20 (2007), 931-967
  • MSC (2000): Primary 16W22; Secondary 20C20
  • DOI: https://doi.org/10.1090/S0894-0347-07-00563-2
  • MathSciNet review: 2328711