Difference Algebra
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Publication:3053882
DOI10.1016/S1570-7954(06)80008-2zbMath1209.12004MaRDI QIDQ3053882
Publication date: 30 October 2010
Published in: Handbook of Algebra (Search for Journal in Brave)
Difference algebra (12H10) Research exposition (monographs, survey articles) pertaining to field theory (12-02)
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Cites Work
- Picard-Vessiot Theory of Linear Homogeneous Difference Equations
- Ideal Theory and Algebraic Difference Equations
- Complete Difference Ideals
- Manifolds of Difference Polynomials
- A theorem on difference polynomials
- Inversive difference fields
- Principal Solutions of Difference Equations
- A note on the singular manifolds of a difference polynomial
- Extensions of Difference Fields
- On Extensions of Difference Fields and the Resolvents of Prime Difference Ideals
- The Manin-Mumford conjecture and the model theory of difference fields
- Multivariable dimension polynomials and new invariants of differential field extensions
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- Specializations over difference fields
- A note on differentially algebraic solutions of first order linear difference equations
- Dimension polynomials of extensions of difference fields
- Valuations and the Ritt problem
- Specializations of differential kernels and the Ritt problem
- Strong normality and normality for difference fields
- The structure of strongly normal difference extensions
- On the Galois theory of difference fields
- Solving difference equations in finite terms
- Difference algebraic subgroups of commutative algebraic groups over finite fields
- An algorithm for computing a standard form for second-order linear \(q\)-difference equations
- Galois theory of difference equations
- Generic automorphisms of fields
- Reducible linear difference operators
- A characterization of linear difference equations which are solvable by elementary operations
- On solutions of linear ordinary difference equations in their coefficient field
- Computations in differential and difference modules
- Computation of Hilbert polynomials in two variables
- Invertibility of causal discrete time dynamical systems
- On an extension of the Picard-Vessiot theory
- Kähler differentials and differential algebra
- A notion of Krull dimension for differential rings
- A bound for the orders of the components of a system of algebraic difference equations
- Linearly reducible linear difference operators
- The inverse Galois problem of extensions of difference fields
- Types of singularity of components of difference polynomials
- Singular manifolds of difference polynomials
- On the group of automorphisms of a function field
- Essential singular manifolds of difference polynomials
- A note on existentially closed difference fields with algebraically closed fixed field
- A note on groups definable in difference fields
- On the set of Hilbert polynomials
- ON DIFFERENCE FIELDS WITH QUANTIFIER ELIMINATION
- Finitely Generated Extensions of Difference Fields
- On the Intersections of the Components of a Difference Polynomial
- An Invariant of Difference Field Extensions
- Finitely Generated Pathological Extensions Of Difference Fields
- Finitely Generated Extensions of Partial Difference Fields
- Automatique en temps discret et algèbre aux différences
- Fundamental solutions for meromorphic linear difference equations in the complex plane, and related problems.
- Solutions in the General Solution of Second Order Algebraic Differential Equations
- Linearization of Discrete-Time Systems
- On Galois Theory of Fields with Operators
- On the Differential Transcendence Polynomials of Finitely Generated Differential Field Extensions
- The Greenspan Bound for the Order of Differential Systems
- Extensions of Difference Specializations
- Summation in Finite Terms
- COMPUTATION OF DIMENSION POLYNOMIALS
- Well-Ordering of Certain Numerical Polynomials
- The General Solution of a First Order Differential Polynomial
- Model theory of difference fields
- Characteristic polynomials of finitely generated modules over Weyl algebras
- Order and Dimension
- On the inverse problem in difference Galois theory
- Algebraic Extensions of Difference Fields
- Kahler Differentials and Differential Algebra in Arbitrary Characteristic
- A recursive algorithm for the computation of the hilbert polynomial
- The Foundations for an Extension of Differential Algebra
- An Existence Theorem for Difference Polynomials
- Solvability of Linear Homogeneous Difference Equations by Elementary Operations
- An Extension of Differential Galois Theory
- The notion of dimension in the theory of algebraic differential equations
- A Note on the Galois Theory of Linear Homogeneous Difference Equations
- Errata: An Existence Theorem for Difference Polynomials
- The Galois Correspondence for Linear Homogeneous Difference Equations
- Systems of Ideals
- Differential Dimension Polynomials and a Fundamental Theorem on Differential Modules
- A Difference-Differential Basis Theorem
- The Existence of Solutions of Abstract Partial Difference Polynomials
- An Improved Result Concerning Singular Manifolds of Difference Polynomials
- Jacobi's Bound for First Order Difference Equations