It was proved in [5] that each weakly d-Koszul module M possesses a natural filtration of graded submodules 0 = Uo C U1 C ? ? ? C Up-1 C Up - M such that all quotients Ui+1/Ui are d-Koszul modules. This paper continues the study of weakly d-Koszul modules. In particular, we have Pn = ?f=1 Pn for all Pn > 0, where P -> Ui/U1x1 -> 0 and V, -> M ->?0 are the corresponding minimal graded projective resolutions, which implies easily that pd(M) -maxi{pd(Ci/Ui-1)} and that the finitistic dimension conjecture is true in the category of weakly d-Koszul modules under certain conditions.
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