Growth of graded noetherian rings
Authors:
Darin R. Stephenson and James J. Zhang
Journal:
Proc. Amer. Math. Soc. 125 (1997), 15931605
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 subexponential 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 GKdimension. 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 Mathematics0112, University of California at San Diego, La Jolla, California 920930112
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/S0002993997037520
PII:
S 00029939(97)037520
Keywords:
Subexponential growth,
GKdimension,
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
