Growth of graded noetherian rings

Stephenson, Darin; Zhang, James

doi:10.1090/S0002-9939-97-03752-0

Growth of graded noetherian rings
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by Darin R. Stephenson and James J. Zhang PDF

Proc. Amer. Math. Soc. 125 (1997), 1593-1605 Request permission

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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