| Title:
|
Regular submodules of torsion modules over a discrete valuation domain (English) |
| Author:
|
Astuti, Pudji |
| Author:
|
Wimmer, Harald K. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
349-357 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A submodule $W$ of a $p$-primary module $M$ of bounded order is known to be regular if $W$ and $M$ have simultaneous bases. In this paper we derive necessary and sufficient conditions for regularity of a submodule. (English) |
| Keyword:
|
regular submodules |
| Keyword:
|
modules over discrete valuation domains |
| Keyword:
|
Abelian $p$-groups |
| Keyword:
|
simultaneous bases |
| MSC:
|
13C12 |
| MSC:
|
20K10 |
| MSC:
|
20K25 |
| idZBL:
|
Zbl 1155.13304 |
| idMR:
|
MR2291741 |
| . |
| Date available:
|
2009-09-24T11:33:37Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128071 |
| . |
| Reference:
|
[1] R. Baer: Types of elements and the characteristic subgroups of Abelian groups.Proc. London Math. Soc. 39 (1935), 481–514. |
| Reference:
|
[2] J. Ferrer, F. Puerta, and X. Puerta: Geometric characterization and classification of marked subspaces.Linear Algebra Appl. 235 (1996), 15–34. MR 1374248, 10.1016/0024-3795(94)00107-3 |
| Reference:
|
[3] L. Fuchs: Infinite Abelian Groups, Vol. I.Academic Press, New York, 1973. MR 0349869 |
| Reference:
|
[4] L. Fuchs: Infinite Abelian Groups, Vol. II.Academic Press, New York, 1973. Zbl 0257.20035, MR 0349869 |
| Reference:
|
[5] I. Kaplanski: Infinite Abelian Groups.University of Michigan Press, Ann Arbor, 1954. MR 0065561 |
| Reference:
|
[6] N. Ya. Vilenkin: Direct decompositions of topological groups, I.Mat. Sbornik N. S. 19 (1946), 85–154. (Russian) MR 0017283 |
| . |
