A lifting problem for DG modules

Abstract Let B = A 〈 X | d X = t 〉 be an extended DG algebra by the adjunction of a variable of positive even degree n, and let N be a semi-free DG B-module that is assumed to be bounded below as a graded module. We prove in this paper that N is liftable to A if Ext B n + 1 ( N , N ) = 0 . Furthermore such a lifting is unique up to DG isomorphisms if Ext B n ( N , N ) = 0 .