FC-modules with an application to cotorsion pairs

Guo, Yonghua

Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 4, pp. 513-519.

Résumé

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.

Détail

Classification : 16D40, 16D80, 16E99
Keywords: character modules; flat modules; cotorsion pairs