Year: 2013
Author: Bo Lu
Communications in Mathematical Research , Vol. 29 (2013), Iss. 1 : pp. 41–50
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-CMR-19027
Communications in Mathematical Research , Vol. 29 (2013), Iss. 1 : pp. 41–50
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: $\mathcal{F}$-Perfect ring $\mathcal{F}$-cover $\mathcal{F}$-perfect module cotorsion theory projective module.