Department of Mathematics-0112, University of California at San Diego, La Jolla, California 92093-0112 ; Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195
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.