(untitled) (Communications in Mathematical Research, 2021)
Let R be a ring, and let (F, C) be a cotorsion theory. In this article, the notion of F-perfect rings is introduced as a nontrial generalization of perfect rings and A-perfect rings. A ring R is said to be right F-perfect if F is projective relative to R for any F ∈ F. We give some characterizations of F-perfect rings. For example, we show that a ring R is right F-perfect if and only if F-covers of finitely generated modules are projective. Moreover, we define F-perfect modules and investigate some properties of them.