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Publications Influence

A primer of algebraic D-modules

- S. C. Coutinho
- Mathematics
- 1995

1. The Weyl algebra 2. Ideal structure of the Weyl algebra 3. Rings of differential operators 4. Jacobian conjectures 5. Modules over the Weyl algebra 6. Differential equations 7. Graded and filtered… Expand

262 24

On the density of algebraic foliations without algebraic invariant sets

- S. C. Coutinho, J. Pereira
- Mathematics
- 2006

Abstract Let X be a smooth complex projective variety of dimension greater than or equal to 2, L an ample line bundle and k ≫ 0 an integer. We prove that a very generic global section of the twisted… Expand

32 4- PDF

Module Structure of Rings of Differential Operators

- S. C. Coutinho, M. P. Holland
- Mathematics
- 1 November 1988

Soit X une k-variete affine irreductible lisse pour k un corps de caracteristique zero et soit #7B-D(X) l'anneau des operateurs differentiels k-lineaires sur X. On montre que chaque ideal a droite de… Expand

8 2

D-SIMPLE RINGS AND SIMPLE D-MODULES

- S. C. Coutinho
- Mathematics
- 1999

We use certain derivations of a polynomial ring, that do not leave any proper nonzero ideal invariant, to construct simple non-holonomic modules over the nth Weyl algebra. This approach extends to… Expand

21 2

Primality Testing and Integer Factorization in Public-Key Cryptography

- S. C. Coutinho
- Mathematics
- Advances in Information Security
- 2004

1 © Number-Theoretic Preliminaries This chapter collects the basics of number theory necessary for understanding the following chapters and algorithms. Some of the covered topics are Euclid’s… Expand

9 2- PDF

On the differential simplicity of polynomial rings

- S. C. Coutinho
- Mathematics
- 15 June 2003

Abstract Commutative differentially simple rings have proved to be quite useful as a source of examples in noncommutative algebra. In this paper we use the theory of holomorphic foliations to… Expand

8 2- PDF

On the classification of simple quadratic derivations over the affine plane

- S. C. Coutinho
- Mathematics
- 15 May 2008

Abstract We classify simple derivations induced by unimodular rows of length 2 whose entries have degree 2, over the ring of complex polynomials in two variables. As part of the proof we give several… Expand

5 1- PDF

Introduction to cryptography (2nd edn), by Johannes A. Buchman. Pp. 335. €39.95, £30.50, $44.95. 2004. ISBN 0 387 20756 2 (Springer).

- S. C. Coutinho
- Philosophy
- 1 March 2006

2 1

The Many Avatars of a Simple Algebra

- S. C. Coutinho
- Mathematics
- 1 August 1997

auspices of deformation theory. In this paper we survey the incarnations of the Weyl algebra associated to several formalisms of quantum mechanics. Beginning with the moment of conception in the… Expand

9 1- PDF

The Quest for Quotient Rings (of Noncommutative Noetherian Rings)

- S. C. Coutinho, J. C. McConnell
- Computer Science, Mathematics
- Am. Math. Mon.
- 1 April 2003

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