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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Growth of graded noetherian rings


Authors: Darin R. Stephenson and James J. Zhang
Journal: Proc. Amer. Math. Soc. 125 (1997), 1593-1605
MSC (1991): Primary 16P90, 16W50, 16E10
MathSciNet review: 1371143
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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.


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Additional 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
Email: zhang@math.washington.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03752-0
PII: S 0002-9939(97)03752-0
Keywords: Sub-exponential growth, GK-dimension, graded ring, global dimension
Received by editor(s): December 5, 1995
Additional Notes: The second author was supported by the NSF
Communicated by: Lance W. Small
Article copyright: © Copyright 1997 American Mathematical Society