| Abstract: | Let $R$ be a ring, and let $(mathcal{F}, C)$ be a cotorsion theory. In this article, thenotion of $mathcal{F}$-perfect rings is introduced as a nontrial generalization of perfect ringsand A-perfect rings. A ring $R$ is said to be right $mathcal{F}$-perfect if $F$ is projective relativeto $R$ for any $F ∈ mathcal{F}$. We give some characterizations of $mathcal{F}$-perfect rings. For example,we show that a ring $R$ is right $mathcal{F}$-perfect if and only if $mathcal{F}$-covers of finitely generatedmodules are projective. Moreover, we define $mathcal{F}$-perfect modules and investigate someproperties of them. |
