Differential and difference algebra
type: Item
instance of: scholarly article
title: Differential and difference algebra
zbMATH Open document ID: 0666.12018
DOI: 10.1007/BF01094866
author: A. V. Mikhalev
author: E. V. Pankrat'ev
published in: Journal of Soviet Mathematics
publication date: 1989-01-01T00:00:00Z
Mathematics Subject Classification ID: 12H05
Mathematics Subject Classification ID: 12H10
Mathematics Subject Classification ID: 12-02
Mathematics Subject Classification ID: 14L40
Mathematics Subject Classification ID: 13N05
zbMATH DE Number: 4089680
zbMATH Keywords: Bibliography
zbMATH Keywords: differential algebraic group
zbMATH Keywords: integration in finite form
zbMATH Keywords: differential Galois theory
zbMATH Keywords: differential algebra
zbMATH Keywords: differential modules
zbMATH Keywords: difference algebra
zbMATH Keywords: differential rings
zbMATH Keywords: differential fields
MaRDI profile type: Publication
cites work: Dimension polynomials of extensions of difference fields
cites work: Q4200495
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cites work: Algebraic aspects of nonlinear differential equations
cites work: Exterior differentiation in Lie algebras
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cites work: On Second Order Linear Differential Equations with Algebraic Solutions on Algebraic Curves
cites work: On Second Order Linear Differential Equations with Algebraic Solutions
cites work: Shorter Notes: Extensions of Derivations
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cites work: Derivations and Automorphisms of Nonassociative Matrix Algebras
cites work: The Derivation Algebra of a Real Division Algebra
cites work: Derivations in Prime Rings
cites work: Lie ideals with regular and nilpotent elements and a result on derivations
cites work: Lie ideals and derivations of prime rings
cites work: On universal derivations
cites work: Universal derivations and universal ring constructions
cites work: On Derivations of Lie Algebras
cites work: Q4107261
cites work: On Galois Theory of Fields with Operators
cites work: On the Inverse Problem of Galois Theory of Differential Fields
cites work: A note to general notions of the derivation and its applications
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cites work: Determination of the differentiably simple rings with a minimal ideal
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cites work: Complete Models of Differential Fields
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cites work: On the Derivation of x n in a Ring
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cites work: Differentially simple rings

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cites work: Differential Algebraic Groups

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cites work: Differential Algebraic Lie Algebras

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cites work: Differential Algebraic Group Structures on the Plane

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cites work: A liouville theorem on integration in finite terms for line integrals∗

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cites work: A normal form and integration in finite terms for a class of elementary functions

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cites work: Height One Differential Ideals in Polynomial Rings

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cites work: Remark on nilpotency of derivations

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cites work: Nil Derivations and Chain Conditions in Prime Rings

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cites work: Semiprime Rings with Nilpotent Derivatives

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cites work: Derivations of higher order and commutativity of rings

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cites work: Nilpotency of Derivations

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cites work: Nilpotency of Derivations. II

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cites work: Nilpotency of Derivatives on an Ideal

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cites work: Corrigendum to the Paper “Nilpotency of Derivations”

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cites work: Derivations and commutativity of rings

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cites work: Types of singularity of components of difference polynomials

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cites work: The General Solution of a First Order Differential Polynomial

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cites work: Specializations of differential kernels and the Ritt problem

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cites work: The Greenspan Bound for the Order of Differential Systems

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cites work: Valuations and the Ritt problem

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cites work: Solutions in the General Solution of Second Order Algebraic Differential Equations

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cites work: Homological properties of the ring of differential polynomials

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cites work: Some Applications of Differential Algebra to Ring Theory

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cites work: Jordan Derivations on Rings

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cites work: The Risch Differential Equation Problem

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cites work: Elementary and Liouvillian solutions of linear differential equations

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cites work: Power series solutions of algebraic differential equations

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cites work: A Natural Structure Theorem for Complex Fields

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cites work: Algebraic Extensions of Difference Fields

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cites work: Finitely Generated Extensions of Partial Difference Fields

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cites work: Sur certaines algèbres de Lie de dérivations

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cites work: On the centralizers of ideals and nil derivations

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cites work: A Goldie theorem for differentiably prime rings

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cites work: Picard-Vessiot Theory of Linear Homogeneous Difference Equations

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cites work: \({\mathcal D}\)-modules et faisceaux pervers dont le support singulier est un croisement normal

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cites work: Derivations in central separable algebras

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cites work: Derivations with nilpotent values

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cites work: Derivations with invertible values in rings with involution

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cites work: Extension of derivations to modules of quotients

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cites work: The derivations of Mn(C)

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cites work: The Derivation Algebra of M48(C)

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cites work: Radical Regularity in Differential Rings

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cites work: Zero divisors in differential rings

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cites work: Polynomials in denumerable indeterminates

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cites work: The nth Roots of Solutions of Linear Ordinary Differential Equations

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cites work: Derivations on Regular Local Rings of Finitely Generated Type

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cites work: Some properties of positive derivations on 𝑓-rings

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cites work: A Note on Derivations

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cites work: A Note on Derivations II

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cites work: A Theorem on Derivations of Prime Rings with Involution

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cites work: Derivations of prime rings having power central values

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cites work: Strong normality and normality for difference fields

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cites work: The structure of strongly normal difference extensions

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cites work: On the Galois theory of difference fields

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cites work: On the inverse problem in difference Galois theory

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cites work: A notion of Krull dimension for differential rings

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cites work: On Spencer's Cohomology Theory for Linear Partial Differential Operators

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cites work: Some homological properties of Spencer's cohomology theory

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cites work: Extensions of Differential Modules Over Formal Power Series Rings

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cites work: Systems of n Partial Differential Equations in n Unknown Functions: the Conjecture of M. Janet

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cites work: Modules of imperfection in differential algebra

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cites work: Order for systems of differential equations and a generalization of the notion of differential ring

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cites work: Prolongation of integral domains

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cites work: Primitive derivations in free associative algebras

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cites work: Lie Rings of Derivations of Associative Rings

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cites work: The Lie Structure of a Commutative Ring with a Derivation

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cites work: Simple Lie Rings of Derivations of Commutative Rings

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cites work: DIFFERENTIALLY SIMPLE RINGS WITH NO INVERTIBLE DERIVATIVES

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cites work: Corrections to : “A conjecture in the arithmetic theory of differential equations”

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cites work: Adjunctions and comonads in differential algebra

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cites work: On the quasi-affine scheme of a differential ring

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cites work: Differential rings constructed from quasi-prime ideals

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cites work: Jacobi's Bound for the Order of Systems of First Order Differential Equations

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cites work: Jacobi's Bound for First Order Difference Equations

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cites work: Extensions of Difference Specializations

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cites work: Lie ideals and derivations in rings with involution

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cites work: Differential Identities in Prime Rings With Involution

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cites work: Derivations with algebraic values

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cites work: Differential simplicity and extensions of a derivation

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cites work: Quelques remarques a propos des s-derivations

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cites work: Derivations et automorphismes algebriques d'Anneaux premiers

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cites work: Ritt's question on the Wronskian

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cites work: Differentially Hilbertian differential fields

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cites work: Differential Specializations in Integral and Algebraic Extensions

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cites work: The Differential Ideals [ y p z ]

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cites work: The Congruence Lemma for [ y p z ]

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cites work: Transcendental constants over the coefficient fields in differential elliptic function fields

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cites work: Derivations of special subrings of matrix rings and regular graphs

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cites work: PRIME IDEAL STRUCTURE IN ADDITIVE CONSERVATIVE SYSTEMS

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cites work: Remarks on maximally differential prime ideals

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cites work: Integral closure of rings of solutions of linear differential equations

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cites work: Lie and Jordan Structure in Prime Rings with Derivations

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cites work: The solution of the problem of integration in finite terms

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cites work: On Liouville's theory of elementary functions

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cites work: On solutions of differential equations which satisfy certain algebraic relations

Differential and difference algebra (cites work)
cites work: Derivationen und Automorphismen von Algebren, in denen die Gleichung \(X^2=0\) nur trivial lösbar ist

Differential and difference algebra (cites work)
cites work: Standard and Alternative Algebras with Completely Reducible Derivation Algebras

Differential and difference algebra (cites work)
cites work: On Derivation Algebras of Malcev Algebras and Lie Triple Systems

Differential and difference algebra (cites work)
cites work: On Derivation Algebras of Malcev Algebras

Differential and difference algebra (cites work)
cites work: Q3779204

Differential and difference algebra (cites work)
cites work: Corrections and supplements to my paper ''Differential modules and derivations of complete discrete valuation rings''

Differential and difference algebra (cites work)
cites work: Higher differential algebras of discrete valuation rings

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cites work: Q3966111

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cites work: Q4198858

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cites work: Q4744382

Differential and difference algebra (cites work)
cites work: Solution of the Inverse Problem of Differential Galois Theory in the Classical Case

Differential and difference algebra (cites work)
cites work: Q4748302

Differential and difference algebra (cites work)
cites work: Sur la commutativite des anneaux differentiels

Differential and difference algebra (cites work)
cites work: Sur la commutativite des anneaux differentiels II

Differential and difference algebra (cites work)
cites work: Q3765940

Differential and difference algebra (cites work)
cites work: First Order Differential Closures of Certain Partially Ordered Fields

Differential and difference algebra (cites work)
cites work: Derivations of PI-algebras and smoothness of noncommutative curves

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cites work: Q3338974

Differential and difference algebra (cites work)
cites work: Differentiability in local fields of prime characteristic

Differential and difference algebra (cites work)
cites work: Extension of derivations

Differential and difference algebra (cites work)
cites work: Notes toward higher differential algebra

Differential and difference algebra (cites work)
cites work: On Lie algebras of differential formal groups of Ritt

Differential and difference algebra (cites work)
cites work: Q3758006

Differential and difference algebra (cites work)
cites work: Prime model extensions for differential fields of characteristic p ≠ 0

Differential and difference algebra (cites work)
cites work: The model theory of differential fields revisited

Differential and difference algebra (cites work)
cites work: DERIVATIONS AND AFFINE STRUCTURES OF SOME NILPOTENT LIE ALGEBRAS

Differential and difference algebra (cites work)
cites work: Differentiably simple rings of prime characteristic

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