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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Growth of graded noetherian rings
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by Darin R. Stephenson and James J. Zhang
Proc. Amer. Math. Soc. 125 (1997), 1593-1605
DOI: https://doi.org/10.1090/S0002-9939-97-03752-0

Abstract:

We show that every graded locally finite right noetherian algebra has sub-exponential growth. As a consequence, every noetherian algebra with exponential growth has no finite dimensional filtration which leads to a right (or left) noetherian associated graded algebra. We also prove that every connected graded right noetherian algebra with finite global dimension has finite GK-dimension. Using this, we can classify all connected graded noetherian algebras of global dimension two.
References
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Bibliographic Information
  • Darin R. Stephenson
  • Affiliation: Department of Mathematics-0112, University of California at San Diego, La Jolla, California 92093-0112
  • Email: dstephen@math.ucsd.edu
  • James J. Zhang
  • Affiliation: Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195
  • MR Author ID: 314509
  • Email: zhang@math.washington.edu
  • Received by editor(s): December 5, 1995
  • Additional Notes: The second author was supported by the NSF
  • Communicated by: Lance W. Small
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 1593-1605
  • MSC (1991): Primary 16P90, 16W50, 16E10
  • DOI: https://doi.org/10.1090/S0002-9939-97-03752-0
  • MathSciNet review: 1371143