(p, λ)-Koszul algebras and modules, II

Abstract

This paper is a continuous work of [14], where the notions of (p, λ)-Koszul algebra and (p, λ)-Koszul module were first introduced. More precisely, some new criteria for a positively graded algebra to be (p, λ) -Koszul are provided. We also generalize (p, λ) -Koszul objects to the nongraded case and define the so-called quasi- (p, λ) -Koszul objects. Further, the relationships between (quasi-) (p, λ) -Koszul modules and minimal Horseshoe Lemma are established.