Abstract
A 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.
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