Difference Algebra

DOI10.1016/S1570-7954(06)80008-2zbMath1209.12004MaRDI QIDQ3053882

Alexander B. Levin

Publication date: 30 October 2010

Published in: Handbook of Algebra (Search for Journal in Brave)

zbMATH Keywords

difference algebradifference Galois theorydifference modulesdifference field extensions

Mathematics Subject Classification ID

Difference algebra (12H10) Research exposition (monographs, survey articles) pertaining to field theory (12-02)

Related Items

Functional relations for solutions of \(q\)-difference equations

Uses Software

• RatDiff

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