Algebras without noetherian filtrations

Authors:
J. T. Stafford and J. J. Zhang

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1329-1338

MSC (2000):
Primary 16P40, 16P90, 16R99, 16W70

DOI:
https://doi.org/10.1090/S0002-9939-02-06972-1

Published electronically:
December 6, 2002

MathSciNet review:
1949861

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Abstract | References | Similar Articles | Additional Information

Abstract: We provide examples of finitely generated noetherian PI algebras for which there is no finite dimensional filtration with a noetherian associated graded ring; thus we answer negatively a question of Lorenz (1988).

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Additional Information

**J. T. Stafford**

Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109

Email:
jts@umich.edu

**J. 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/S0002-9939-02-06972-1

Keywords:
PI algebra,
noetherian filtration,
associated graded ring

Received by editor(s):
September 25, 2000

Published electronically:
December 6, 2002

Additional Notes:
Both authors were supported in part by the NSF. The second author was also supported by the Royalty Research Fund of the University of Washington

Communicated by:
Lance W. Small

Article copyright:
© Copyright 2002
American Mathematical Society