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Ring Theory pp 165–177Cite as

Differential operators on commutative algebras

Part of the Lecture Notes in Mathematics book series (LNM,volume 1197)

Abstract

This article discusses some of the similarities/differences between the theory of differential operators on (a) a non-singular variety in characteristic zero (b) a non-singular variety in positive characteristic (c) a singular variety in characteristic zero.

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References

  1. J.N. BERNSTEIN, I.M. GELFAND, S.I. GELFAND, Differnetial Operators on the cubic cone, Russian Math Surveys, 27 (1972) 169–174.

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  2. J.E. BJORK, Rings of Differential Operators, North-Holland Mathematical Library, Amsterdam (1979).

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  3. W.C. BROWN, A note on higher derivations and ordinary points of curves, Rocky Mountain Journal Math., 14 (1984) 397–402.

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  5. A. GROTHENDIECK, Elements de Geometrie Algebrique IV, Inst. des Hautes Etudes Sci., Publ. Math. No. 32 (1967).

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  6. S.P. SMITH, Differential Operators on the Affine and Projective Lines in Characteristic P>0, Seminaire M.P. Malliavin, to appear.

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  7. S.P. SMITH, The Global Homological Dimension of Differential Operators on a non-singular variety over a field of positive characteristic, J. Algebra (to appear).

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  8. S.P. SMITH, J.T. STAFFORD, Differential Operators on an Affine Curve, in preparation.

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  9. M.E. SWEEDLER, Groups of Simple Algebras, Publ. Math. IHES, No. 44 (1975).

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© 1986 Springer-Verlag

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Smith, S.P. (1986). Differential operators on commutative algebras. In: van Oystaeyen, F.M.J. (eds) Ring Theory. Lecture Notes in Mathematics, vol 1197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076323

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  • DOI: https://doi.org/10.1007/BFb0076323

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16496-8

  • Online ISBN: 978-3-540-39833-2

  • eBook Packages: Springer Book Archive