Two remarks about Picard-Vessiot extensions and elementary functions
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TL;DRAbstract
We present a simple proof of the theorem which says that for a series of extensions of differential fields K ⊂ L ⊂ M, where K ⊂ M is Picard-Vessiot, the extension K ⊂ L is Picard-Vessiot iff the differential Galois group $Gal_{L} M$ is a normal subgroup o
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We present a simple proof of the theorem which says that for a series of extensions of differential fields K ⊂ L ⊂ M, where K ⊂ M is Picard-Vessiot, the extension K ⊂ L is Picard-Vessiot iff the differential Galois group $Gal_{L} M$ is a normal subgroup o
Keywords
MathematicsExtension (predicate logic)Galois groupPure mathematicsDifferential Galois theoryDifferential (mechanical device)Simple (philosophy)Algebra over a field
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