Quasi-d-Koszul Modules and Applications

Let R be a Noetherian semiperfect algebra. A necessary and sufficient condition for a finitely generated R-module to be quasi-d-Koszul is given, which improves one of the main results in 1]. The authors also give a necessary and sufficient condition for the Minimal Horseshoe Lemma holding in mod(R). As an application, it is proved that the “Minimal Horseshoe Lemma” is true in the category of quasi-d-Koszul modules under certain conditions.