F-perfect Rings and Modules

摘要

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.