Generalization of quasi-Koszul algebras

Abstract

In this paper, we generalize two kinds of graded algebras, δ-Koszul algebras andKp algebras, to the non-graded cases. The trivial modules of δ-Koszul algebras have pure resolutions, while those of Kp algebras admit non-pure resolutions. We provide necessary and sufficient conditions for a notherian semiperfect algebra either to be a quasi-δ-Koszul algebra or to be a quasi-Kp algebra. confusion.) Then the mapinduced by θ is a monomorphism, and hence, split (since the domain and codomain of the map are semisimple). Let ζ be the A/J-module morphism Ω m (K n /JK n )/JΩ m (K n /JK n ) → K n+m /JK n+m such that ζ •θ = 1.Combining these diagrams, we have the following commutative diagram 0 / / K n+m θ / / P n+m−1