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).
@article{108004,
author = {Peter Vassilev Danchev},
title = {A note on the countable extensions of separable $p\sp {\omega+n}$-projective abelian $p$-groups},
journal = {Archivum Mathematicum},
volume = {042},
year = {2006},
pages = {251-254},
zbl = {1152.20045},
mrnumber = {2260384},
language = {en},
url = {http://dml.mathdoc.fr/item/108004}
}
Danchev, Peter Vassilev. A note on the countable extensions of separable $p\sp {\omega+n}$-projective abelian $p$-groups. Archivum Mathematicum, Tome 042 (2006) pp. 251-254. http://gdmltest.u-ga.fr/item/108004/
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