# Relative D-groups and differential Galois theory in several derivations

@article{Snchez2012RelativeDA, title={Relative D-groups and differential Galois theory in several derivations}, author={Omar Le{\'o}n S{\'a}nchez}, journal={Transactions of the American Mathematical Society}, year={2012}, volume={367}, pages={7613-7638} }

The Galois theory of logarithmic differential equations with respect to relative D-groups in partial differential-algebraic geometry is developed.

## 8 Citations

On the model companion of partial differential fields with an automorphism

- Mathematics
- 2013

We prove that the class of partial differential fields of characteristic zero with an automorphism has a model companion. We then establish the basic model theoretic properties of this theory and…

DIFFERENCE ALGEBRAIC RELATIONS AMONG SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS

- MathematicsJournal of the Institute of Mathematics of Jussieu
- 2015

We extend and apply the Galois theory of linear differential equations equipped with the action of an endomorphism. The Galois groups in this Galois theory are difference algebraic groups, and we use…

SOME DEFINABLE GALOIS THEORY AND EXAMPLES

- Computer Science, MathematicsThe Bulletin of Symbolic Logic
- 2017

Improve the definitions and results on generalized strongly normal extensions from [Pillay, “Differential Galois theory I”, Illinois Journal of Mathematics, 42(4), 1998], using this to give a restatement of a conjecture on almost semiabelian δ-groups.

On parameterized differential Galois extensions

- Mathematics
- 2016

Abstract We prove some existence results on parameterized strongly normal extensions for logarithmic equations. We generalize a result in Wibmer (2012) [16] . We also consider an extension of the…

DIFFERENTIAL-ALGEBRAIC JET SPACES PRESERVE

- Mathematics
- 2015

3 Abstract. Suppose p is the generic type of a differential-algebraic jet space to a finite dimensional 4 differential-algebraic variety at a generic point. It is shown that p satisfies a certain…

DIFFERENTIAL-ALGEBRAIC JET SPACES PRESERVE INTERNALITY TO THE CONSTANTS

- Mathematics, Computer ScienceThe Journal of Symbolic Logic
- 2015

It is shown that p satisfies a certain strengthening of almost internality to the constants, which is a model-theoretic abstraction of the generic behaviour of jet spaces in complex-analytic geometry.

Action of an endomorphism on (the solutions of) a linear differential equation

- Publications Mathématiques de Besançon
- 2019

—The purpose of this survey is to provide the reader with a user friendly introduction to the two articles [8] and [9], which give a Galoisian description of the action of an endomorphism of a…

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