TY - JOUR
T1 - $\mathcal{F}$-Perfect Rings and Modules
AU - Lu , Bo
JO - Communications in Mathematical Research 
VL - 1
SP - 41
EP - 50
PY - 2021
DA - 2021/05
SN - 29
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19027.html
KW - $\mathcal{F}$-Perfect ring, $\mathcal{F}$-cover, $\mathcal{F}$-perfect module, cotorsion theory, projective
module.
AB - <p style="text-align: justify;">Let $R$ be a ring, and let $(\mathcal{F}, C)$ be a cotorsion theory. In this article, the
notion of $\mathcal{F}$-perfect rings is introduced as a nontrial generalization of perfect rings
and A-perfect rings. A ring $R$ is said to be right $\mathcal{F}$-perfect if $F$ is projective relative
to $R$ 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 generated
modules are projective. Moreover, we define $\mathcal{F}$-perfect modules and investigate some
properties of them.</p>