On Koszul Algebras and a New Construction of Artin–Schelter Regular Algebras

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.