Naïve liftings of DG modules

Let n be a positive integer, and let A strongly commutative differential graded (DG) algebra over ring R. Assume that In this paper, we study naïve liftability of DG modules along the natural injection $$A\rightarrow B$$ using notions diagonal ideals homotopy limits. We prove if N is bounded below semifree B-module such $${\text {Ext}}_B ^i (N, N)=0$$ for all $$i\geqslant 1$$ , then naïvely liftable to A. This implies direct summand Also, relation between Auslander-Reiten Conjecture has been described.