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K-theory of Noetherian rings

Part of the Lecture Notes in Mathematics book series (LNM,volume 1404)

Keywords

  • Noetherian Ring
  • Matrix Ring
  • Weyl Algebra
  • Cyclic Homology
  • Trace Group

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References

  1. J. Alev, "Actions de groupes sur A1(ℂ)", in Ring Theory LNM 1197, Springer New York 1986.

    Google Scholar 

  2. J.Alev, T.J.Hodges and J.Velez "Fixed rings of Weyl algebras", preprint, University of Cincinnati, 1987.

    Google Scholar 

  3. M. Auslander and D.A. Buchsbaum, "On ramification theory in Noetherian rings", Amer. J. Math., 81 (1959), 749–764.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. A. Beilinson and I.N. Bernstein, "Localization de g-modules" C.R. Acad. Sci. Paris Ser. I 292 (1981), 15–18.

    MathSciNet  MATH  Google Scholar 

  5. A. Beilinson and I.N. Bernstein, "A generalisation of Casselman's submodule theorem", Representation theory of reductive groups, Birkhauser, Boston 1983.

    MATH  Google Scholar 

  6. A. Borel, Linear Algebraic Groups, Benjamin, New York 1969.

    MATH  Google Scholar 

  7. K.S. Brown and S.M. Gersten, "Algebraic K-theory as generalized sheaf cohomology" in Algebraic K-theory 1, LNM 341 Springer, New York 1973.

    Google Scholar 

  8. B.H. Dayton and C.A. Weibel, "A Spectral Sequence for the K-theory of Affine Glued Schemes" in Algebraic K-theory, Evanston 1980, LNM 854 Springer, New York 1981.

    Google Scholar 

  9. J. Dixmier, "Sur les algebres de Weyl", Bull. Soc. Math. France, 96 (1968), 209–242.

    MathSciNet  MATH  Google Scholar 

  10. P. Gabriel, "Des catégories abéliennes", Bull. Soc. Math. France, 90 (1962), 323–448.

    MathSciNet  MATH  Google Scholar 

  11. K. R. Goodearl, "Simple Noetherian rings not isomorphic to matrix rings over domains", Comm. in Alg., 12 1984, 1421–1435.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. R. Hartshorne, Algebraic Geometry, Springer-Verlag, New York 1977.

    CrossRef  MATH  Google Scholar 

  13. T.J. Hodges, "K-theory and right ideal class groups for HNP rings", Trans. Amer. Math. Soc., 302 (1987), 751–767.

    MathSciNet  MATH  Google Scholar 

  14. T.J.Hodges, "Equivariant K-theory of Noetherian rings," J. London Math. Soc., to appear.

    Google Scholar 

  15. T.J.Hodges, "A noncommutative Bass-Tate sequence," Bull. Soc. Math. Belg., to appear.

    Google Scholar 

  16. T.J.Hodges, "Equivariant K-theory of Noetherian schemes", preprint, University of Cincinnati, 1987.

    Google Scholar 

  17. T.J. Hodges and S.P. Smith, "Rings of differential operators and the Bernstein-Beilinson equivalence" of categories, Proc. Amer. Math. Soc., 93 (1985), 379–386.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. T.J. Hodges and S.P. Smith, "The global dimension of certain primitive factors of the enveloping algebra of a semi-simple Lie algebra", J. London Math. Soc. (2), 82 (1985), 411–418.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. T.J.Hodges and S.P.Smith, ""Differential operators on projective space", preprint, University of Cincinnati 1985.

    Google Scholar 

  20. T.J. Hodges and J. Osterburg, "An indecomposable projective module over a Noetherian domain of Krull dimension one", Bull. London Math. Soc., 19 (1987), 139–144.

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. A. Joseph, "On the classification of primitive ideals in the enveloping algebra of a semisimple Lie algebra", in Lie Group Representations I, LNM 1024 Springer, New York.

    Google Scholar 

  22. A. Joseph and J.T. Stafford, "Modules of ł-finite vectors over semi-simple Lie algebras", Proc. London Math. Soc. (3), 49 (1984), 361–384.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. M. Karoubi, "Homologie cyclique et K-théorie algébrique 1", C. R. Acad. Sci. Paris, Ser.I, 297 (1983), 447–450.

    MathSciNet  MATH  Google Scholar 

  24. M.E. Keating, "On the theory of tiled orders", J. Algebra, 43 (1976), 193–197.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. L. LeBruyn, "Towards a noncommutative version of the Bass-Tate sequence", Bull. Soc. Math. Belg. Ser. B, 35 (1983), 45–67.

    MathSciNet  Google Scholar 

  26. T. Levasseur, "Anneaux d'opérateurs differentiels", Seminaire d'algebre Malliavin, LNM 867 Springer, New York 1981.

    Google Scholar 

  27. M. Lorenz, "K0 of skew group rings and simple Noetherian rings without idempotents", J. London Math. Soc. (2), 32 (1985), 41–50.

    CrossRef  MathSciNet  MATH  Google Scholar 

  28. M. Lorenz, "Frobenius reciprocity and G0 of skew group rings", preprint, Max-Planck-Institut 1986.

    Google Scholar 

  29. D. Milicic, "Localization and representation theory of reductive Lie groups", lecture notes, University of Utah 1987, to appear.

    Google Scholar 

  30. S. Montgomery, Fixed Rings of Finite Automorphism Groups of Associative Rings, LNM 818, Springer, Berlin 1980.

    CrossRef  MATH  Google Scholar 

  31. D.S. Passman, The algebraic structure of group rings, Wiley, New York (1977).

    MATH  Google Scholar 

  32. D. Quillen, "Higher Algebraic K-theory" in Algebraic K-Theory, LNM 341, Springer, Berlin 1973.

    Google Scholar 

  33. J.C. Robson, "Idealisers and Hereditary Noetherian Prime Rings", J. Algebra, 22 (1972), 45–81.

    CrossRef  MathSciNet  MATH  Google Scholar 

  34. J.J. Rotman, An introduction to homological algebra, Academic Press, New York 1979.

    MATH  Google Scholar 

  35. L. Silver, "Non-commutative localization and applications", J. Algebra, 7 (1967), 44–76.

    CrossRef  MathSciNet  MATH  Google Scholar 

  36. J.T. Stafford, "Generating modules efficiently: algebraic K-theory for noncommutative Noetherian rings", J. Algebra, 69 (1981), 312–335.

    CrossRef  MathSciNet  MATH  Google Scholar 

  37. B. Stenstrom, Rings of Quotients, Springer Verlag, Berlin 1975.

    CrossRef  MATH  Google Scholar 

  38. A.E. Zalesskii and O.M. Neroslavskii, "There exists a simple Noetherian ring with divisors of zero but without idempotents", Comm. Alg. 5 (1977), 231–234.

    CrossRef  MathSciNet  Google Scholar 

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© 1989 Springer-Verlag

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Hodges, T.J. (1989). K-theory of Noetherian rings. In: Malliavin, MP. (eds) Séminaire d’Algèbre Paul Dubreil et Marie-Paul Malliavin. Lecture Notes in Mathematics, vol 1404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084079

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  • DOI: https://doi.org/10.1007/BFb0084079

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