| Title:
|
Relatively exact modules (English) |
| Author:
|
Bican, Ladislav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
44 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
569-576 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Rim and Teply [10] investigated relatively exact modules in connection with the existence of torsionfree covers. In this note we shall study some properties of the lattice $\Cal E_{\tau}(M)$ of submodules of a torsionfree module $M$ consisting of all submodules $N$ of $M$ such that $M/N$ is torsionfree and such that every torsionfree homomorphic image of the relative injective hull of $M/N$ is relatively injective. The results obtained are applied to the study of relatively exact covers of torsionfree modules. As an application we also obtain some new characterizations of perfect torsion theories. (English) |
| Keyword:
|
Hereditary torsion theory $\tau$ |
| Keyword:
|
$\tau$-injective module |
| Keyword:
|
$\tau$-exact module |
| Keyword:
|
preradical |
| Keyword:
|
exact torsion theory |
| Keyword:
|
perfect torsion theory |
| MSC:
|
16D50 |
| MSC:
|
16D80 |
| MSC:
|
16S90 |
| MSC:
|
18E40 |
| idZBL:
|
Zbl 1101.16023 |
| idMR:
|
MR2062873 |
| . |
| Date available:
|
2009-01-08T19:31:13Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119411 |
| . |
| Reference:
|
[1] Anderson F.W., Fuller K.R.: Rings and Categories of Modules.Graduate Texts in Mathematics, vol.13 Springer-Verlag (1974). Zbl 0301.16001, MR 0417223 |
| Reference:
|
[2] Bican L.: Torsionfree precovers.to appear. Zbl 1074.16002, MR 2080845 |
| Reference:
|
[3] Bican L., El Bashir R., Enochs E.: All modules have flat covers.Proc. London Math. Society 33 (2001), 649-652. Zbl 1029.16002, MR 1832549 |
| Reference:
|
[4] Bican L., Torrecillas B.: Precovers.Czechoslovak Math. J. 53 (128) (2003), 191-203. Zbl 1016.16003, MR 1962008 |
| Reference:
|
[5] Bican L., Torrecillas B.: On covers.J. Algebra 236 (2001), 645-650. Zbl 0973.16002, MR 1813494 |
| Reference:
|
[6] Bican L., Torrecillas B.: On the existence of relative exact covers.Acta Math. Hungar. 95 (2002), 178-186. MR 1905180 |
| Reference:
|
[7] Bican L., Torrecillas B.: Relative exact covers.Comment. Math. Univ. Carolinae 42 (2001), 477-487. Zbl 1068.16039, MR 1883369 |
| Reference:
|
[8] Bican L., Kepka T., Němec P.: Rings, Modules, and Preradicals.Marcel Dekker New York (1982). MR 0655412 |
| Reference:
|
[9] Golan J.: Torsion Theories.Pitman Monographs and Surveys in Pure an Applied Mathematics, 29 Longman Scientific and Technical (1986). Zbl 0657.16017, MR 0880019 |
| Reference:
|
[10] Rim S.H., Teply M.L.: On coverings of modules.Tsukuba J. Math. 24 (2000), 15-20. Zbl 0985.16017, MR 1791327 |
| Reference:
|
[11] García Rozas J.R., Torrecillas B.: On the existence of covers by injective modules relative to a torsion theory.Comm. Algebra 24 (1996), 1737-1748. MR 1386494 |
| Reference:
|
[12] Teply M.L.: Torsion-free covers II.Israel J. Math. 23 (1976), 132-136. Zbl 0321.16014, MR 0417245 |
| Reference:
|
[13] Xu J.: Flat Covers of Modules.Lecture Notes in Mathematics 1634 Springer Verlag, Berlin-Heidelberg-New York (1996). Zbl 0860.16002, MR 1438789 |
| . |
