| Title:
|
On direct sums of $\text{B}^{(1)}$-groups -- II (English) |
| Author:
|
De Vivo, Clorinda |
| Author:
|
Metelli, Claudia |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
47 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
189-202 |
| . |
| Category:
|
math |
| . |
| Summary:
|
$\operatorname{B}^{(1)}$-groups are a class of torsionfree Abelian groups of finite rank, part of the main class of Butler groups. In the paper C. Metelli, {\it On direct sums of $\operatorname{B}^{(1)}$-groups\/}, Comment. Math. Univ. Carolinae {\bf 34} (1993), 587--591, the problem of direct sums of $\operatorname{B}^{(1)}$-groups was discussed, and a necessary and sufficient condition was given for the direct sum of two $\operatorname{B}^{(1)}$-groups to be a $\operatorname{B}^{(1)}$-group. While sufficiency holds, necessity was wrongly claimed; we solve here the problem, and in the process study a curious hierarchy among indecomposable direct summands of $\operatorname{B}^{(1)}$-groups. (English) |
| Keyword:
|
Butler group |
| Keyword:
|
$\operatorname{B}^{(1)}$-group |
| Keyword:
|
tent |
| Keyword:
|
direct decomposition |
| Keyword:
|
finite algorithm |
| MSC:
|
20K15 |
| idZBL:
|
Zbl 1106.20041 |
| idMR:
|
MR2241526 |
| . |
| Date available:
|
2009-05-05T16:56:42Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119586 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/118616 |
| . |
| Reference:
|
[FII] Fuchs L.: Infinite Abelian Groups. Vol.II.Academic Press London - New York (1973). Zbl 0257.20035, MR 0349869 |
| Reference:
|
[A] Arnold D.M.: Abelian groups and representations of finite partially ordered sets.CMS books in Mathematics Springer New York (2000). Zbl 0959.16011, MR 1764257 |
| Reference:
|
[AV] Arnold D.M., Vinsonhaler C.: Finite rank Butler groups: a survey of recent results.Abelian groups (Curaçao, 1991) Dekker New York (1993), 17-41. Zbl 0804.20043, MR 1217256 |
| Reference:
|
[M] Metelli C.: On direct sums of ${an{B^{(1)}}}$-groups.Comment. Math. Univ. Carolinae 34 (1993), 587-591. MR 1243091 |
| Reference:
|
[DVM4] De Vivo C., Metelli C.: Decomposing ${an{B^{(1)}}}$-groups: an algorithm..Comm. Algebra 30 (2002), 12 5621-5637. MR 1941915 |
| Reference:
|
[DVM8] De Vivo C., Metelli C.: On degenerate ${an{B^{(2)}}}$-groups.Houston J. Math., to appear. MR 2247900 |
| Reference:
|
[CDVM] Caruso I., De Vivo C., Metelli C.: Partition bases for ${an{B^{(1)}}}$-groups.to appear on Abelian Groups, Rings and Modules; Lecture Notes in Pure and Applied Mathematics, Taylor and Francis, 2005. |
| . |
