Growth of graded noetherian rings
Darin R. Stephenson and James J. Zhang
Proc. Amer. Math. Soc. 125 (1997), 1593-1605
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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Darin R. Stephenson
Department of Mathematics-0112, University of California at San Diego, La Jolla, California 92093-0112
James J. Zhang
Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195
Received by editor(s):
December 5, 1995
The second author was supported by the NSF
Lance W. Small
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American Mathematical Society