Let $R$ be a ring, $n$ an non-negative integer and $d$ positive or $\infty$. A right $R$-module $M$ is called \emph{$(n,d)^*$-projective} if ${\rm Ext}^1_R(M, C)=0$ for every $n$-copresented $C$ of injective dimension $\leq d$; ring \emph{right $(n,d)$-cocoherent} with $id(C)\leq d$ $(n+1)$-copresented; $(n,d)$-cosemihereditary} whenever $0\rightarrow C\rightarrow E\rightarrow A\rightarrow 0$ e...

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...