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:
https://doi.org/10.1090/S0002-9939-97-03752-0

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