Koszul modules and Gorenstein algebras (Q1911795)

The author introduces Koszul modules. The first part of the paper is devoted to the study of their properties. Then it is proved that if \(A\) is a local or a graded CM ring, a Gorenstein algebra of codimension one or two over \(A\) is a Koszul module. This generalizes a well-known statement for rank one modules. Then a structure theorem for Gorenstein algebras of codimension one or two over a local or graded CM ring is obtained.