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A primer of algebraic D-modules
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 filteredExpand
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On the density of algebraic foliations without algebraic invariant sets
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 twistedExpand
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Module Structure of Rings of Differential Operators
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 deExpand
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D-SIMPLE RINGS AND SIMPLE D-MODULES
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 toExpand
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Primality Testing and Integer Factorization in Public-Key Cryptography
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’sExpand
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On the differential simplicity of polynomial rings
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 toExpand
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On the classification of simple quadratic derivations over the affine plane
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 severalExpand
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The Many Avatars of a Simple Algebra
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 theExpand
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The Quest for Quotient Rings (of Noncommutative Noetherian Rings)
TLDR
Goldie’s theorems on quotient rings in the context of the life and times of the man who discovered them. Expand
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