| Title:
|
Precovers (English) |
| Author:
|
Bican, Ladislav |
| Author:
|
Torrecillas, Blas |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
1 |
| Year:
|
2003 |
| Pages:
|
191-203 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\mathcal G$ be an abstract class (closed under isomorpic copies) of left $R$-modules. In the first part of the paper some sufficient conditions under which $\mathcal G$ is a precover class are given. The next section studies the $\mathcal G$-precovers which are $\mathcal G$-covers. In the final part the results obtained are applied to the hereditary torsion theories on the category on left $R$-modules. Especially, several sufficient conditions for the existence of $\sigma $-torsionfree and $\sigma $-torsionfree $\sigma $-injective covers are presented. (English) |
| Keyword:
|
precover |
| Keyword:
|
cover |
| Keyword:
|
(pre)cover class of modules |
| Keyword:
|
hereditary torsion theory |
| Keyword:
|
relatively injective modules |
| MSC:
|
16D50 |
| MSC:
|
16D90 |
| MSC:
|
16S90 |
| idZBL:
|
Zbl 1016.16003 |
| idMR:
|
MR1962008 |
| . |
| Date available:
|
2009-09-24T11:00:22Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127790 |
| . |
| Reference:
|
[1] L. Bican, T. Kepka and P. Němec: Rings, Modules, and Preradicals.Marcel Dekker, New York, 1982. MR 0655412 |
| Reference:
|
[2] E. Enochs: Torsion free covering modules II.Proc. Amer. Math. Soc. 114 (1963), 884–889. MR 0168617, 10.1090/S0002-9939-1963-0168617-7 |
| Reference:
|
[3] J. Golan: Torsion Theories.Pitman Monographs and Surveys in Pure an Applied Matematics, vol. 29, Longman Scientific and Technical, 1986. Zbl 0657.16017, MR 0880019 |
| Reference:
|
[4] J. R. García Rozas and B. Torrecillas: On the existence of covers by injective modules relative to a torsion theory.Comm. Algebra 24 (1996), 1737–1748. MR 1386494, 10.1080/00927879608825667 |
| Reference:
|
[5] J. Rada and M. Saorín: Rings characterized by (pre)envelopes and (pre)covers of their modules.Comm. Algebra 26 (1998), 899–912. MR 1606190, 10.1080/00927879808826172 |
| Reference:
|
[6] M. Teply: Torsionfree injective modules.Pacific J. Math. 28 (1969), 441–453. MR 0242878, 10.2140/pjm.1969.28.441 |
| Reference:
|
[7] M. Teply: Torsion-free covers II.Israel J. Math. 23 (1976), 132–136. Zbl 0321.16014, MR 0417245, 10.1007/BF02756792 |
| Reference:
|
[8] B. Torrecillas: T-torsionfree T-injective covers.Comm. Algebra 12 (1984), 2707–2726. MR 0757788, 10.1080/00927878408823128 |
| Reference:
|
[9] J. Xu: Flat Covers of Modules.Lecture Notes in Mathematics, 1634 Springer Verlag, Berlin-Heidelberg-New York, 1996. Zbl 0860.16002, MR 1438789 |
| . |
