| Title:
|
FC-modules with an application to cotorsion pairs (English) |
| Author:
|
Guo, Yonghua |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
50 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
513-519 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
character modules |
| Keyword:
|
flat modules |
| Keyword:
|
cotorsion pairs |
| MSC:
|
16D40 |
| MSC:
|
16D80 |
| MSC:
|
16E99 |
| idZBL:
|
Zbl 1203.16008 |
| idMR:
|
MR2583129 |
| . |
| Date available:
|
2009-12-22T08:03:19Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137442 |
| . |
| Reference:
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