| Title:
|
A note on the countable extensions of separable $p\sp {\omega+n}$-projective abelian $p$-groups (English) |
| Author:
|
Danchev, Peter |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
42 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
251-254 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is proved that if $G$ is a pure $p^{\omega + n}$-projective subgroup of the separable abelian $p$-group $A$ for $n\in {N}\cup \lbrace 0\rbrace $ such that $|A/G|\le \aleph _0$, then $A$ is $p^{\omega +n}$-projective as well. This generalizes results due to Irwin-Snabb-Cutler (CommentṀathU̇nivṠtṖauli, 1986) and the author (Arch. Math. (Brno), 2005). (English) |
| Keyword:
|
countable extensions |
| Keyword:
|
separable groups |
| Keyword:
|
$p^{\omega +n}$-projective groups |
| MSC:
|
20K10 |
| idZBL:
|
Zbl 1152.20045 |
| idMR:
|
MR2260384 |
| . |
| Date available:
|
2008-06-06T22:48:19Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108004 |
| . |
| Reference:
|
[1] Danchev, P.: Countable extensions of torsion abelian groups.Arch. Math. (Brno) 41(3) (2005), 265–273. Zbl 1114.20030, MR 2188382 |
| Reference:
|
[2] Irwin, J., Snabb, T. and Cutler, D.: On $p^{\omega +n}$-projective $p$-groups.Comment. Math. Univ. St. Pauli 35(1) (1986), 49–52. MR 0838187 |
| Reference:
|
[3] Nunke, R.: Purity and subfunctors of the identity.Topics in Abelian Groups, Scott, Foresman and Co., 1963, 121–171. MR 0169913 |
| Reference:
|
[4] Nunke, R.: Homology and direct sums of countable abelian groups.Math. Z. 101(3) (1967), 182–212. Zbl 0173.02401, MR 0218452 |
| Reference:
|
[5] Wallace, K.: On mixed groups of torsion-free rank one with totally projective primary components.J. Algebra 17(4) (1971), 482–488. Zbl 0215.39902, MR 0272891 |
| . |
