# A note on the countable extensions of separable ${p}^{\omega +n}$-projective abelian $p$-groups

Archivum Mathematicum (2006)

- Volume: 042, Issue: 3, page 251-254
- ISSN: 0044-8753

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topDanchev, Peter Vassilev. "A note on the countable extensions of separable $p^{\omega +n}$-projective abelian $p$-groups." Archivum Mathematicum 042.3 (2006): 251-254. <http://eudml.org/doc/249795>.

@article{Danchev2006,

abstract = {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).},

author = {Danchev, Peter Vassilev},

journal = {Archivum Mathematicum},

keywords = {countable extensions; separable groups; $p^\{\omega +n\}$-projective groups; countable extensions; separable groups; projective groups; pure projective subgroups; separable Abelian -groups},

language = {eng},

number = {3},

pages = {251-254},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {A note on the countable extensions of separable $p^\{\omega +n\}$-projective abelian $p$-groups},

url = {http://eudml.org/doc/249795},

volume = {042},

year = {2006},

}

TY - JOUR

AU - Danchev, Peter Vassilev

TI - A note on the countable extensions of separable $p^{\omega +n}$-projective abelian $p$-groups

JO - Archivum Mathematicum

PY - 2006

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 042

IS - 3

SP - 251

EP - 254

AB - 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).

LA - eng

KW - countable extensions; separable groups; $p^{\omega +n}$-projective groups; countable extensions; separable groups; projective groups; pure projective subgroups; separable Abelian -groups

UR - http://eudml.org/doc/249795

ER -

## References

top- Countable extensions of torsion abelian groups, Arch. Math. (Brno) 41(3) (2005), 265–273. Zbl1114.20030MR2188382
- On ${p}^{\omega +n}$-projective $p$-groups, Comment. Math. Univ. St. Pauli 35(1) (1986), 49–52. MR0838187
- Purity and subfunctors of the identity, Topics in Abelian Groups, Scott, Foresman and Co., 1963, 121–171. MR0169913
- Homology and direct sums of countable abelian groups, Math. Z. 101(3) (1967), 182–212. Zbl0173.02401MR0218452
- On mixed groups of torsion-free rank one with totally projective primary components, J. Algebra 17(4) (1971), 482–488. Zbl0215.39902MR0272891

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