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Growth of graded noetherian rings
Author(s):
Darin
R.
Stephenson;
James
J.
Zhang
Journal:
Proc. Amer. Math. Soc.
125
(1997),
1593-1605.
MSC (1991):
Primary 16P90, 16W50, 16E10
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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:
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
Copyright of article:
Copyright
1997,
American Mathematical Society
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