Pacific Journal of Mathematics

Rings of differential operators on one-dimensional algebras.

Marc Chamarie and Ian M. Musson

Article information

Source
Pacific J. Math., Volume 147, Number 2 (1991), 269-290.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102644910

Mathematical Reviews number (MathSciNet)
MR1084709

Zentralblatt MATH identifier
0713.16014

Subjects
Primary: 16S32: Rings of differential operators [See also 13N10, 32C38]
Secondary: 13N10: Rings of differential operators and their modules [See also 16S32, 32C38] 16D90: Module categories [See also 16Gxx, 16S90]; module theory in a category-theoretic context; Morita equivalence and duality

Citation

Chamarie, Marc; Musson, Ian M. Rings of differential operators on one-dimensional algebras. Pacific J. Math. 147 (1991), no. 2, 269--290. https://projecteuclid.org/euclid.pjm/1102644910


Export citation

References

  • [I] M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley (1969).
  • [2] I. N. Bernstein, I. M. Gefand and S. I. Gel'fand, Differential operators on the cubic cone, Russian Math. Surveys, 27 (1972), 169-174.
  • [3] J. E. Bjork, Rings of Differential Operators,North-Holland(1979).
  • [4] A. Borel et al., Algebraic D-Modules, Perspectivesin Mathematics, Vol. 2, Aca- demic Press (1987).
  • [5] J. Dieudonne,Topics in Local Algebra,University of Notre Dame Press (1967).
  • [6] R. Hartshorne, Algebraic Geometry, Springer Graduate Text in Mathematics No. 52, Springer-Verlag (1977).
  • [7] Y. Ishibashi, A characterization of one dimensional regular local rings in terms of high order derivations, Bull. Fukuoka Univ. Ed., 24 (1974), 11-18.
  • [8] I. Kaplansky, Commutative Rings, University of Chicago Press, (1974).
  • [9] K. R. Mount and O. E. Villamayor, On a conjecture of Y. Nakai, Osaka J. Math., 10(1973), 325-327.
  • [10] J. L. Muhasky, The differential operator ring of an affine curve, Trans. Amer. Math. Soc, 307 (1988), 705-723.
  • [II] I. M. Musson, Rings of differential operators and zero divisors,J. Algebra, 125 (1989), 489-501.
  • [12] D. W. Sharpe and P. Vamos, Injective Modules, Cambridge University Press, (1972).
  • [13] S. P. Smith, Curves, Differential Operators and Finite Dimensional Algebras, pp. 158-176, Sem. d'Algebre Paul Dubreil et M. P. Malliavin, Lecture Notes in Mathematics, vol. 1296, Springer-Verlag, 1987.
  • [14] S. P. Smith, The simple 2) -module associated to the intersection homology com- plex for a class of plane curves, J. Pure Appl. Algebra, 50 (1988), 287-294.
  • [15] S. P. Smith and J. T. Stafford, Differential operators on an affine curve, Proc. London Math. Soc, 56 (1988), 229-259.