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2010-09-13

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Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/35151

Galois Theory of Module Fields

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[eng] This thesis is about Galois theory. The development of a Galois theory for differential equations analogous to the classical Galois theory for polynomial equations was already an aim of S. Lie in the 19th century. The first step in this direction was the development of a Galois theory for linear differential equations due to E. Picard and E. Vessiot. Later, B.H. Matzat and M. van der Put created a theory for iterative differential equations in positive characteristic. H. Umemura constructed a Galois theory for algebraic differential equations in characteristic zero. There also exist analog theories for difference equations, starting with a theory for linear difference equations till the one due to S. Morikawa and H. Umemura for algebraic difference equations. M. Takeuchi, K. Amano and A. Masuoka unified Galois theories for linear differential and linear difference equations using the language of module algebras. This thesis has two goals. The first is the development of a more general Galois theory that combines the capacity of the theories of H. Umemura and S. Morikawa, which allow the treatment of field extensions of big generality, with the advantage of the formulation of K. Amano and A. Masuoka, which unifies structures like derivations and automorphisms. The second goal is the removal of the restriction to fields of characteristic zero from the theories of H. Umemura and S. Morikawa. KEY WORDS: Galois Theory, Differential Equation, Difference Equation, Module Algebra

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Teoria de Galois, Equacions diferencials

Matèries (anglès)

Galois theory, Differential equations

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Tesis Doctorals - Departament - Algebra i Geometria

Citació

HEIDERICH, Florian. Galois Theory of Module Fields. [consulta: 11 de desembre de 2025]. [Disponible a: https://hdl.handle.net/2445/35151]

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