A lifting problem for DG modules

Let B = A < X vertical bar dX = 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. (C) 2020 Published by Elsevier Inc.