On the Definitions of Difference Galois Groups

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129285We compare several definitions of the Galois group of a linear difference equation that have arisen in algebra, analysis and model theory and show, that these groups are isomorphic over suitable fields. In addition, we study properties of Picard-Vessiot extensions over fields with not necessarily algebraically closed subfields of constants.Classical Analysis and ODEsLogic12H10; 03C60; 12L12; 39A13On the Definitions of Difference Galois Groupstext