In this note, we investigate the relationship between almost projective modules and generalized modules. These concepts are useful for study on finite direct sum of lifting It is proved that; if M N-projective any N, then N-projective. We also show that N lifting, im-small discuss question when again lifting.

Finitely-hollow lifting and hollow-weak modules are two generalizations of hollow module which is a weaker version module. In this paper, we have defined another generalization hollow-lifting namely finitely-hollow-weak (f-hollow-weak lifting) Various properties been seen found that, it not closed under quotients summands in general, so sufficient conditions provided f-hollow-weak property inhe...

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