| Title:
|
Quasi-balanced torsion-free groups (English) |
| Author:
|
Goeters, H. Pat |
| Author:
|
Ullery, William |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
3 |
| Year:
|
1998 |
| Pages:
|
431-443 |
| . |
| Category:
|
math |
| . |
| Summary:
|
An exact sequence $0\to A\to B\to C\to 0$ of torsion-free abelian groups is quasi-balanced if the induced sequence $$ 0\to \bold Q\otimes\operatorname{Hom}(X,A)\to\bold Q\otimes\operatorname{Hom}(X,B) \to\bold Q\otimes\operatorname{Hom}(X,C)\to 0 $$ is exact for all rank-1 torsion-free abelian groups $X$. This paper sets forth the basic theory of quasi-balanced sequences, with particular attention given to the case in which $C$ is a Butler group. The special case where $B$ is almost completely decomposable gives rise to a descending chain of classes of Butler groups. This chain is a generalization of the chain of Kravchenko classes that arise from balanced sequences. As an application of our results concerning quasi-balanced sequences, the relationship between the two chains in the quasi-category of torsion-free abelian groups is illuminated. (English) |
| Keyword:
|
quasi-balanced |
| Keyword:
|
almost balanced |
| Keyword:
|
Kravchenko classes |
| MSC:
|
20K15 |
| MSC:
|
20K25 |
| MSC:
|
20K27 |
| MSC:
|
20K35 |
| MSC:
|
20K40 |
| idZBL:
|
Zbl 0968.20027 |
| idMR:
|
MR1666837 |
| . |
| Date available:
|
2009-01-08T18:45:03Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119022 |
| . |
| Reference:
|
[A1] Arnold D.: Pure subgroups of finite rank completely decomposable groups.Abelian Group Theory Lecture Notes in Math. 874 Springer-Verlag New York (1982), 1-31. MR 0645913 |
| Reference:
|
[A2] Arnold D.: Finite Rank Torsion-Free Abelian Groups and Rings.Lecture Notes in Math. 931 Springer-Verlag New York (1982). Zbl 0493.20034, MR 0665251 |
| Reference:
|
[AV] Arnold D., Vinsonhaler C.: Pure subgroups of finite rank completely decomposable groups $anII$.Abelian Group Theory Lecture Notes in Math. 1006 Springer-Verlag New York (1983), 97-143. MR 0722614 |
| Reference:
|
[B] Butler M.C.R.: A class of torsion-free abelian groups of finite rank.Proc. London Math. Soc. 15 (1965), 680-698. Zbl 0131.02501, MR 0218446 |
| Reference:
|
[F] Fuchs L.: Infinite Abelian Groups.II Academic Press New York (1973). Zbl 0257.20035, MR 0349869 |
| Reference:
|
[K] Kravchenko A.A.: Balanced and cobalanced Butler groups.Math. Notes Acad. Sci. USSR 45 (1989), 369-373. Zbl 0695.20032, MR 1005459 |
| Reference:
|
[NV1] Nongxa L.G., Vinsonhaler C.: Balanced Butler groups.J. Algebra, to appear. Zbl 0846.20060, MR 1378545 |
| Reference:
|
[NV2] Nongxa L.G., Vinsonhaler C.: Balanced representations of partially ordered sets.to appear. |
| Reference:
|
[V] C. Vinsonhaler: A survey of balanced Butler groups and representations.Abelian Groups and Modules Lecture Notes in Pure and Applied Math. 182 Marcel Dekker (1996), 113-122. Zbl 0865.20040, MR 1415625 |
| . |
