On a general difference Galois theory I

Abstract

We know well difference Picard-Vessiot theory, Galois theory of linear difference equations. We propose a general Galois theory of difference equations that generalizes Picard-Vessiot theory. For every difference field extension of characteristic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>0</mml:mn> </mml:math> , we attach its Galois group, which is a group of coordinate transformation.