Krull dimension of modules and involutive ideals

Coutinho, S. C.

doi:10.1090/S0002-9939-1995-1243163-9

Krull dimension of modules and involutive ideals
HTML articles powered by AMS MathViewer

by S. C. Coutinho

Proc. Amer. Math. Soc. 123 (1995), 1647-1654

DOI: https://doi.org/10.1090/S0002-9939-1995-1243163-9

PDF | Request permission

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.

References

Joseph Bernstein and Valery Lunts, On nonholonomic irreducible $D$-modules, Invent. Math. 94 (1988), no. 2, 223–243. MR 958832, DOI 10.1007/BF01394325
J.-E. Björk, Rings of differential operators, North-Holland Mathematical Library, vol. 21, North-Holland Publishing Co., Amsterdam-New York, 1979. MR 549189
Ofer Gabber, The integrability of the characteristic variety, Amer. J. Math. 103 (1981), no. 3, 445–468. MR 618321, DOI 10.2307/2374101
Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157, DOI 10.1007/978-1-4757-3849-0
G. R. Krause and T. H. Lenagan, Growth of algebras and Gel′fand-Kirillov dimension, Research Notes in Mathematics, vol. 116, Pitman (Advanced Publishing Program), Boston, MA, 1985. MR 781129
Ernst Kunz, Introduction to commutative algebra and algebraic geometry, Birkhäuser Boston, Inc., Boston, MA, 1985. Translated from the German by Michael Ackerman; With a preface by David Mumford. MR 789602
Valery Lunts, Algebraic varieties preserved by generic flows, Duke Math. J. 58 (1989), no. 3, 531–554. MR 1016433, DOI 10.1215/S0012-7094-89-05824-9
J. C. McConnell and J. C. Robson, Noncommutative Noetherian rings, Pure and Applied Mathematics (New York), John Wiley & Sons, Ltd., Chichester, 1987. With the cooperation of L. W. Small; A Wiley-Interscience Publication. MR 934572
J. T. Stafford, Nonholonomic modules over Weyl algebras and enveloping algebras, Invent. Math. 79 (1985), no. 3, 619–638. MR 782240, DOI 10.1007/BF01388528
Pierre Schapira, Microdifferential systems in the complex domain, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 269, Springer-Verlag, Berlin, 1985. MR 774228, DOI 10.1007/978-3-642-61665-5