Generalized Koszul algebra and Koszul duality

We define generalized Koszul modules and rings develop a theory for N-graded with the degree zero part noetherian semiperfect. This specializes to classical graded artinian semisimple developed by Beilinson-Ginzburg-Soergel ungraded semiperfect Green Martinéz-Villa. Let A be left finite ring generated in 1 A0 semiperfect, J its Jacobson radical. By dual of we mean Yoneda Ext Ext_A•(A/J,A/J). If is M module, then it proved that associated GrJA module GrJM. locally algebra, following statements are equivalent: Koszul; Ext_A•(A/J,A/J) (classically) opposite Aop Koszul. As an application, if global dimension AS regular only self-injective.