On Koszul algebras and a new construction of Artin-Schelter regular algebras

Abstract

We prove the simple fact that the factor ring of a Koszul algebra by a regular, normal, quadratic element is a Koszul algebra. This fact leads to a new construction of quadratic Artin-Schelter regular algebras. This construction generalizes the construction of Artin-Schelter regular Clifford algebras. © 2001 Academic Press.