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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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  • 1. A. V. Jategaonkar, Localization in Noetherian Rings, CUP, Cambridge, 1986. MR 88c:16005
  • 2. A. V. Jategaonkar, Morita duality and noetherian rings, J. Algebra, 69 (1981), 358-371. MR 82j:16036
  • 3. G. R. Krause and T. H. Lenagan, Growth of Algebras and Gelfand-Kirillov Dimension (Revised edition), Graduate Studies in Mathematics, 22, Amer. Math. Soc., Providence, RI, 2000. MR 2000j:16035
  • 4. H. Li and F. Van Oystaeyen, Zariskian filtrations. Comm. in Algebra, 17 (1989), 2945-2970. MR 90m:16004
  • 5. H. Li and F. Van Oystaeyen, Zariskian Filtrations. K-Monographs in Mathematics, Kluwer Academic Publishers, Dordrecht, 1996. MR 97m:16083
  • 6. M. Lorenz, On Gelfand-Kirillov dimension and related topics, J. Algebra, 118 (1988), 423-437. MR 89m:16004
  • 7. M. Lorenz, Gelfand-Kirillov Dimension and Poincaré Series, Cuadernos de Algebra, No.7, Universidad de Grenada, Grenada, 1988.
  • 8. J. C. McConnell and J. C . Robson, Noncommutative Noetherian Rings, Wiley, Chichester, 1987. MR 89j:16023
  • 9. J. J. Rotman, An Introduction to Homological Algebra, Academic Press, New York, 1979. MR 80k:18001
  • 10. J. T. Stafford and N. R. Wallach, The restriction of admissible modules to parabolic subalgebras, Trans. Amer. Math. Soc., 272 (1982), 333-350. MR 83h:17007
  • 11. J. T. Stafford and J. J. Zhang, Homological properties of (graded) noetherian PI rings, J. Algebra, 168 (1994), 988-1026. MR 95h:16030
  • 12. D. R. Stephenson and J. J. Zhang, Growth of graded noetherian rings, Proc. Amer. Math. Soc., 125 (1997), 1593-1605. MR 97g:16033
  • 13. Q. Wu and J. J. Zhang, Homological identities for noncommutative rings, J. Algebra, 242 (2001), 516-535. MR 2002k:16011
  • 14. A. Yekutieli, Dualizing complexes over noncommutative graded algebras, J. Algebra, 153 (1992), 41-84. MR 94a:16077
  • 15. A. Yekutieli and J. J. Zhang, Rings with Auslander dualizing complexes, J. Algebra, 213 (1999), 1-51. MR 2000f:16012

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Additional Information

J. T. Stafford
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109

J. J. Zhang
Affiliation: Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195

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

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