On extensions of primary almost totally projective abelian groups

Peter Vassilev Danchev

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

Peter Vassilev Danchev (2006)

Archivum Mathematicum

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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 $n \in N \cup {0}$ such that $| A / G | \leq ℵ_{0}$ , 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).

On countable extensions of primary abelian groups

Peter Vassilev Danchev (2007)

Archivum Mathematicum

Similarity:

It is proved that if $A$ is an abelian $p$ -group with a pure subgroup $G$ so that $A / G$ is at most countable and $G$ is either $p^{ω + n}$ -totally projective or $p^{ω + n}$ -summable, then $A$ is either $p^{ω + n}$ -totally projective or $p^{ω + n}$ -summable as well. Moreover, if in addition $G$ is nice in $A$ , then $G$ being either strongly $p^{ω + n}$ -totally projective or strongly $p^{ω + n}$ -summable implies that so is $A$ . This generalizes a classical result of Wallace (J. Algebra, 1971) for totally projective $p$ -groups as well as continues our recent investigations...

Displaying similar documents to “On extensions of primary almost totally projective abelian groups”

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

On countable extensions of primary abelian groups

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