Previous |  Up |  Next

Article

Title: On torsionfree classes which are not precover classes (English)
Author: Bican, Ladislav
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 58
Issue: 2
Year: 2008
Pages: 561-568
Summary lang: English
.
Category: math
.
Summary: In the class of all exact torsion theories the torsionfree classes are cover (precover) classes if and only if the classes of torsionfree relatively injective modules or relatively exact modules are cover (precover) classes, and this happens exactly if and only if the torsion theory is of finite type. Using the transfinite induction in the second half of the paper a new construction of a torsionfree relatively injective cover of an arbitrary module with respect to Goldie’s torsion theory of finite type is presented. (English)
Keyword: hereditary torsion theory
Keyword: exact
Keyword: noetherian and perfect torsion theory
Keyword: Goldie’s torsion theory
Keyword: precover class
Keyword: cover class
Keyword: precover and cover of a module
MSC: 16D50
MSC: 16D90
MSC: 16S90
MSC: 18E40
idZBL: Zbl 1166.16013
idMR: MR2411109
.
Date available: 2009-09-24T11:56:57Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/128277
.
Reference: [1] F. W. Anderson and K. R. Fuller: Rings and Categories of Modules.Graduate Texts in Mathematics, Springer-Verlag, 1974. MR 0417223
Reference: [2] L. Bican: Torsionfree precovers.Contributions to General Algebra 15, Proceedings of the Klagenfurt Conference 2003 (AAA 66), Verlag Johannes Heyn, Klagenfurt 2004 15 (2004), 1–6. Zbl 1074.16002, MR 2080845
Reference: [3] L. Bican: Relatively exact modules.Comment. Math. Univ. Carolinae 44 (2003), 569–574. Zbl 1101.16023, MR 2062873
Reference: [4] L. Bican: Precovers and Goldie’s torsion theory.Math. Bohem. 128 (2003), 395–400. Zbl 1057.16027, MR 2032476
Reference: [5] L. Bican: On precover classes.Ann. Univ. Ferrara Sez. VII Sc. Mat. LI (2005), 61–67. Zbl 1122.16001, MR 2294759
Reference: [6] L. Bican, R. El Bashir and E. Enochs: All modules have flat covers.Proc. London Math. Society 33 (2001), 649–652. MR 1832549
Reference: [7] L. Bican and B. Torrecillas: Precovers.Czech. Math. J. 53 (2003), 191–203. MR 1962008
Reference: [8] L. Bican and B. Torrecillas: On covers.J. Algebra 236 (2001), 645–650. MR 1813494, 10.1006/jabr.2000.8562
Reference: [9] L. Bican and B. Torrecillas: On the existence of relative injective covers.Acta Math. Hungar. 95 (2002), 178–186. MR 1905180
Reference: [10] L. Bican and B. Torrecillas: Relative exact covers.Comment. Math. Univ. Carolinae 42 (2001), 477–487. MR 1883369
Reference: [11] L. Bican, T. Kepka and P. Němec: Rings, Modules, and Preradicals.Marcel Dekker, New York, 1982. MR 0655412
Reference: [12] J. Golan: Torsion Theories.Pitman Monographs and Surveys in Pure an Applied Matematics, 29, Longman Scientific and Technical, 1986. Zbl 0657.16017, MR 0880019
Reference: [13] J. R. García Rozas and B. Torrecillas: On the existence of covers by injective modules relative to a torsion theory.Comm. Alg. 24 (1996), 1737–1748. MR 1386494, 10.1080/00927879608825667
Reference: [14] S. H. Rim and M. L. Teply: On coverings of modules.Tsukuba J. Math. 24 (2000), 15–20. MR 1791327
Reference: [15] M. L. Teply: Torsion-free covers II.Israel J. Math. 23 (1976), 132–136. Zbl 0321.16014, MR 0417245
Reference: [16] M. L. Teply: Some aspects of Goldie’s torsion theory.Pacif. J. Math. 29 (1969), 447–459. Zbl 0174.06803, MR 0244323, 10.2140/pjm.1969.29.447
Reference: [17] J. Xu: Flat Covers of Modules.Lecture Notes in Mathematics 1634, Springer Verlag Berlin-Heidelberg-New York, 1996. Zbl 0860.16002, MR 1438789
.

Files

Files Size Format View
CzechMathJ_58-2008-2_19.pdf 230.6Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo