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Krull dimension of modules and involutive ideals

Author: S. C. Coutinho
Journal: Proc. Amer. Math. Soc. 123 (1995), 1647-1654
MSC: Primary 16S32; Secondary 16P90
MathSciNet review: 1243163
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Abstract: In this paper we establish an upper bound for the Krull dimension of a module over a Weyl algebra in terms of a geometrical invariant of its characteristic variety, the involutive dimension. This is followed by some examples which show that this inequality may be strict.

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  • [1] J. Bernstein and V. Lunts, On non-holonomic irreducible D-modules, Invent. Math. 94 (1988), 223-243. MR 958832 (90b:58247)
  • [2] J.-E. Björk, Rings of differential operators, North-Holland, Amsterdam, 1979. MR 549189 (82g:32013)
  • [3] O. Gabber, The integrability of the characteristic variety, Amer. J. Math. 103 (1981), 445-465. MR 618321 (82j:58104)
  • [4] R. Hatshorne, Algebraic geometry, Springer-Verlag, New York and Berlin, 1977. MR 0463157 (57:3116)
  • [5] G. R. Krause and T. Lenagan, Growth of algebras and Gelfand-Kirillov dimension, Pitman, London, 1985. MR 781129 (86g:16001)
  • [6] E. Kunz, Introduction to commutative algebra and algebraic geometry, Birkhäuser, Boston, 1985. MR 789602 (86e:14001)
  • [7] V. Lunts, Algebraic varieties preserved by generic flows, Duke Math. J. 58 (1989), 531-554. MR 1016433 (91a:32015)
  • [8] J. C. McConnell and J. C. Robson, Noncommutative noetherian rings, Wiley, London, 1988. MR 934572 (89j:16023)
  • [9] J. T. Stafford, Non-holonomic modules over Weyl algebras and enveloping algebras, Invent. Math. 79 (1985), 619-638. MR 782240 (86h:17009)
  • [10] P. Schapira, Microdifferential systems in the complex domain, Springer-Verlag, Berlin and Heidelberg, 1985. MR 774228 (87k:58251)

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