A note on the countable extensions of separable p ω + n -projective abelian p -groups

Peter Vassilev Danchev

Archivum Mathematicum (2006)

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

Abstract

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It is proved that if G is a pure p ω + n -projective subgroup of the separable abelian p -group A for n ∈ N ∪ { 0 } such that | A / G | ≤ ℵ 0 , then A is p ω + n -projective as well. This generalizes results due to Irwin-Snabb-Cutler (CommentṀathU̇nivṠtṖauli, 1986) and the author (Arch. Math. (Brno), 2005).

How to cite

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Danchev, 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

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  1. Countable extensions of torsion abelian groups, Arch. Math. (Brno) 41(3) (2005), 265–273. Zbl1114.20030MR2188382
  2. On p ω + n -projective p -groups, Comment. Math. Univ. St. Pauli 35(1) (1986), 49–52. MR0838187
  3. Purity and subfunctors of the identity, Topics in Abelian Groups, Scott, Foresman and Co., 1963, 121–171. MR0169913
  4. Homology and direct sums of countable abelian groups, Math. Z. 101(3) (1967), 182–212. Zbl0173.02401MR0218452
  5. 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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