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NONHOLONOMIC SIMPLE D-MODULES FROM SIMPLE DERIVATIONS

Published online by Cambridge University Press:  01 January 2007

S. C. COUTINHO
S. C. COUTINHO*
Affiliation:
Departamento de Ciência da Computação, Instituto de Matemática, Universidade Federal do Rio de Janeiro, P.O. Box 68530, 21945-970 Rio de Janeiro, RJ, BrazilPrograma de Engenharia de Sistemas e Computação, COPPE, UFRJ, PO Box 68511, 21941-972, Rio de Janeiro, RJ, Brazil e-mail: [email protected]
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Abstract.

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We give new examples of affine sufaces whose rings of coordinates are d-simple and use these examples to construct simple nonholonomic D-modules over these surfaces.

Keywords

Primary: 13N1513N10Secondary: 16S32
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 49 , Issue 1 , January 2007 , pp. 11 - 21
Copyright
Copyright © Glasgow Mathematical Journal Trust 2007

References

REFERENCES

1.Archer, J., Derivations on commutative rings and projective modules over skew polynomial rings, PhD thesis, Leeds University (1981).Google Scholar
2.Brumatti, P., Lequain, Y. and Levcovitz, D., Differential simplicity in polynomial rings and algebraic independence of power series, J. London Math. Soc. (2) 68 (2003), 615–630.CrossRefGoogle Scholar
3.Coutinho, S. C., A primer of algebraic D-modules, London Mathematical Society Student Texts 33 (Cambridge University Press, 1995).CrossRefGoogle Scholar
4.Coutinho, S. C., d-simple rings and simple D-modules, Math. Proc. Cambridge Phil. Soc. 125 (1999), 405–415.CrossRefGoogle Scholar
5.Coutinho, S. C., On the differential simplicity of polynomial rings, J. Algebra 264 (2003), 442–468.CrossRefGoogle Scholar
6.Coutinho, S. C., Indecomposable non-holonomic D-modules in dimension 2, Proc. Edinburgh Math. Soc. (2) 46 (2003), 341–355.CrossRefGoogle Scholar
7.Coutinho, S. C., Non-holonomic irreducible D-modules over complete intersections, Proc. Amer. Math. Soc. 131 (2003), 83–86.CrossRefGoogle Scholar
8.Coutinho, S. C. and Menasché, L.Schechter, Algebraic solutions of holomorphic foliations: an algorithmic approach, J. Symbolic Computation 41 (5) (2006), 603–618.CrossRefGoogle Scholar
9.Doering, A. M., Lequain, Y. and Ripoll, C. C., Differential simplicity and cyclic maximal left ideals of the Weyl algebra A 2(K), Glasgow Math. J. 48 (2006), 269–274.CrossRefGoogle Scholar
10.Jordan, D., Differentiably simple rings with no invertible derivatives, Quart. J. Math. Oxford Ser. 2, 32 (1981), 417–424.CrossRefGoogle Scholar
11.Jouanolou, J. P., Equations de Pfaff algébriques Lecture Notes in Mathematics No. 708 (Springer-Verlag, 1979).CrossRefGoogle Scholar
12.Goodearl, K. R. and Warfield, R. B., An introduction to noncommutative noetherian rings, London Mathematical Society Texts 16 (Cambridge University Press, 1989).Google Scholar
13.Maciejewski, A., Moulin-Ollagnier, J. and Nowicki, A., Simple quadratic derivations in two variables, Comm. Algebra 29 (2001), 619–638.CrossRefGoogle Scholar
14.Mc Connell, J. C. and Robson, J. C., Noncommutative Noetherian rings (John Wiley & Sons, Chichester, 1987); revised edition by the American Mathematical Society, Providence, 2001.Google Scholar
15.Mendes, L. G., Algebraic foliations without algebraic solutions, An. Acad. bras. Ci. 69 (1997), 11–13.Google Scholar
16.Nowicki, A., An example of a simple derivation in two variables, preprint.Google Scholar
17.Shioda, T., On the Picard number of a complex projective variety, Ann. Scient. Éc. Norm. Sup., 4e série, 14 (1981), 303–321.CrossRefGoogle Scholar