  The main objective of this paper is to generalize a notion of Koszul
resolutions and charcterizing modules which admits such a resolution. We turn
out that for a noetherian ring $A$ and a coherent $A$ module $M$, $M$ has a two
dimensional generalized Koszul resolution if and only if $M$ is a pure weight
two module in the sense of \cite{HM09}.

Commutative Algebra