Geodesic
FC-modules with an application to cotorsion pairs
Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 4, pp. 513-519 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Let $R$ be a ring. A left $R$-module $M$ is called an FC-module if $M^{+}= \operatorname{Hom}_{\mathbb{Z}}(M, \mathbb{Q}/\mathbb{Z})$ is a flat right $R$-module. In this paper, some homological properties of FC-modules are given. Let $n$ be a nonnegative integer and $\mathcal{FC}_{n}$ the class of all left $R$-modules $M$ such that the flat dimension of $M^{+}$ is less than or equal to $n$. It is shown that $({^{\bot}(\mathcal{FC}_{n}^{\bot})}, \mathcal{FC}_{n}^{\bot})$ is a complete cotorsion pair and if $R$ is a ring such that $\operatorname{fd}(({_RR})^{+})\leq n$ and $\mathcal{FC}_{n}$ is closed under direct sums, then $(\mathcal{FC}_{n}, \mathcal{FC}_{n}^{\bot})$ is a perfect cotorsion pair. In particular, some known results are obtained as corollaries.
Let $R$ be a ring. A left $R$-module $M$ is called an FC-module if $M^{+}= \operatorname{Hom}_{\mathbb{Z}}(M, \mathbb{Q}/\mathbb{Z})$ is a flat right $R$-module. In this paper, some homological properties of FC-modules are given. Let $n$ be a nonnegative integer and $\mathcal{FC}_{n}$ the class of all left $R$-modules $M$ such that the flat dimension of $M^{+}$ is less than or equal to $n$. It is shown that $({^{\bot}(\mathcal{FC}_{n}^{\bot})}, \mathcal{FC}_{n}^{\bot})$ is a complete cotorsion pair and if $R$ is a ring such that $\operatorname{fd}(({_RR})^{+})\leq n$ and $\mathcal{FC}_{n}$ is closed under direct sums, then $(\mathcal{FC}_{n}, \mathcal{FC}_{n}^{\bot})$ is a perfect cotorsion pair. In particular, some known results are obtained as corollaries.
Classification : 16D40, 16D80, 16E99
Keywords: character modules; flat modules; cotorsion pairs 
@article{CMUC_2009_50_4_a1,
     author = {Guo, Yonghua},
     title = {FC-modules with an application to cotorsion pairs},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {513--519},
     year = {2009},
     volume = {50},
     number = {4},
     mrnumber = {2583129},
     zbl = {1203.16008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2009_50_4_a1/}
}
TY  - JOUR
AU  - Guo, Yonghua
TI  - FC-modules with an application to cotorsion pairs
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2009
SP  - 513
EP  - 519
VL  - 50
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/CMUC_2009_50_4_a1/
LA  - en
ID  - CMUC_2009_50_4_a1
ER  - 
%0 Journal Article
%A Guo, Yonghua
%T FC-modules with an application to cotorsion pairs
%J Commentationes Mathematicae Universitatis Carolinae
%D 2009
%P 513-519
%V 50
%N 4
%U http://geodesic.mathdoc.fr/item/CMUC_2009_50_4_a1/
%G en
%F CMUC_2009_50_4_a1
Guo, Yonghua. FC-modules with an application to cotorsion pairs. Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 4, pp. 513-519. http://geodesic.mathdoc.fr/item/CMUC_2009_50_4_a1/