A generalized depth formula for modules of finite quasi-projective dimension

In this paper, we present a generalized formulation of the depth formula for modules over Noetherian local rings, with an emphasis on quasi-projective dimension, extending the classical result of the depth formula originally demonstrated by Auslander, which involved projective dimension. Thus, we replace projective dimension with quasi-projective dimension and show that the general version of the depth formula remains valid under these conditions. This generalization of the depth formula allows us to obtain new consequences and applications.