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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: December 6, 2002
MathSciNet review: 1949861
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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: http://dx.doi.org/10.1090/S0002-9939-02-06972-1
PII: S 0002-9939(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