@Article{CMR-29-41,
author = {Lu , Bo},
title = {$\mathcal{F}$-Perfect Rings and Modules},
journal = {Communications in Mathematical Research },
year = {2021},
volume = {29},
number = {1},
pages = {41--50},
abstract = {<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>},
issn = {2707-8523},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/cmr/19027.html}
}