| Title:
|
QTAG torsionfree modules (English) |
| Author:
|
Bican, Ladislav |
| Author:
|
Torrecillas, Blas |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
1 |
| Year:
|
1992 |
| Pages:
|
1-20 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The structure theory of abelian $p$-groups does not depend on the properties of the ring of integers, in general. The substantial portion of this theory is based on the fact that a finitely generated $p$-group is a direct sum of cyclics. Given a hereditary torsion theory on the category $R$-{\bf Mod} of unitary left $R$-modules we can investigate torsionfree modules having the corresponding property for all torsionfree factor-modules (and a natural requirement concerning extensions of some homomorphisms). This paper continues in our previous investigations of the structural properties of such modules. (English) |
| Keyword:
|
torsion theory |
| Keyword:
|
torsionfree module |
| Keyword:
|
$\sigma$-QTAG-module |
| Keyword:
|
kernel of purity |
| Keyword:
|
center of purity |
| MSC:
|
16D70 |
| MSC:
|
16D80 |
| MSC:
|
16S90 |
| idZBL:
|
Zbl 0765.16009 |
| idMR:
|
MR1173740 |
| . |
| Date available:
|
2009-01-08T17:49:40Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118464 |
| . |
| Reference:
|
[AN] Albu T., Nastasescu C.: Relative finiteness in module theory.Pure and Appl. Math. 84, Marcel Dekker, New York, 1984. Zbl 0556.16001, MR 0749933 |
| Reference:
|
[B$_{1}$] Bican L.: Kulikov's criterion for modules.J. Reine Angew. Math. 288 (1976), 154-159. Zbl 0333.16021, MR 0422320 |
| Reference:
|
[B$_{2}$] Bican L.: The structure of primary modules.Acta Math. Universitatis Carolinae 17 (1976), 3-12. Zbl 0395.16027, MR 0435119 |
| Reference:
|
[BN] Bican L., Kepka T., Němec P.: Rings, Modules and Preradicals.Marcel Dekker, New York, 1982. MR 0655412 |
| Reference:
|
[BT$_{1}$] Bican L., Torrecillas B.: A general Kulikov's theorem.Comm. in Algebra 19 (1990), 2453-2486. MR 1125182 |
| Reference:
|
[BT$_{2}$] Bican L., Torrecillas B.: A relative Ulm's theorem.to appear in Rivista Mat. Pura Appl. Zbl 0779.16013 |
| Reference:
|
[G] Golan J.S.: Torsion Theories.Pitman Monographs and Surveys in Pure and Appl. Math., Longman Scientific Publishing, London, 1986. Zbl 0695.16021, MR 0880019 |
| Reference:
|
[MS] Mehran H., Singh S.: On $\sigma $-pure submodules of QTAG-modules.Arch. Math. 46 (1986), 501-510. Zbl 0596.16021, MR 0849855 |
| Reference:
|
[S$_{1}$] Singh S.: Modules over H.N.P. rings.Can. J. Mat. XXVII (1975), 867-883. MR 0389958 |
| Reference:
|
[S$_{2}$] Singh S.: Some decompositions theorems in abelian groups and their generalizations.In: Ring Theory: Proc. of Ohio University Conf., Lecture Notes in Pure and Applied Math., Marcel Dekker 25 (1986), 183-189. MR 0435146 |
| Reference:
|
[S$_{3}$] Singh S.: Abelian groups like modules.Acta Math. Hungarica 50 (1987), 85-97. Zbl 0628.16014, MR 0893248 |
| Reference:
|
[S] Stenström B.: Rings of Quotients.Springer, Berlin, 1975. MR 0389953 |
| Reference:
|
[T] Teply M.L.: Modules semicocritical with respect to a torsion theory and their applications.Israel J. Math. 54 (1986), 181-200. Zbl 0603.16022, MR 0852477 |
| Reference:
|
[T$_{1}$] Torrecillas B.: On Kulikov's theorem.Comm. in Algebra 14 (1986), 1091-1110. Zbl 0592.16017, MR 0837272 |
| Reference:
|
[T$_{2}$] Torrecillas B.: Height relative to a torsion theory.Ring theory (Antwerp 1985), Lecture Notes in Math. 1197, Springer, Berlin, 1986. Zbl 0589.16021, MR 0859395 |
| Reference:
|
[T$_{3}$] Torrecillas B.: Neat submodules by relative height.Comm. in Algebra 17 (1989), 2309-2324. Zbl 0683.16023, MR 1016867 |
| . |
