# Wydawnictwa / Banach Center Publications / Wszystkie tomy

## Picard-Vessiot theory in general Galois theory

### Tom 94 / 2011

Banach Center Publications 94 (2011), 263-293 MSC: Primary 12H05; Secondary 12H10. DOI: 10.4064/bc94-0-19

#### Streszczenie

We give a transparent proof that difference Picard-Vessiot theory is a part of the general difference Galois theory. We apply the proof to iterative $q$-difference Picard-Vessiot theory to show that Picard-Vessiot theory for iterative $q$-difference field extensions is in the scope of the general Galois theory of Heiderich. We also show that Picard-Vessiot theory is commutative in the sense that studying linear difference-differential equations, no matter how twisted the operators are, we cannot encounter quantification of the Galois groupoid.

#### Autorzy

• Hiroshi UmemuraGraduate School of Mathematics
Chikusa-ku
Nagoya, 464-8602, Japan
e-mail

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