2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144335A double Ore extension is a natural generalization of the Ore extension. We prove that a connected graded double Ore extension of an Artin-Schelter regular algebra is Artin-Schelter regular. Some other basic properties such as the determinant of the DE-data are studied. Using the double Ore extension, we construct 26 families of Artin-Schelter regular algebras of global dimension four in a sequel paper.Rings and Algebras16S36, 16W50, 16A62text