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On extensions of primary almost totally projective abelian groups

Peter Vassilev Danchev (2008)

Mathematica Bohemica

Suppose G is a subgroup of the reduced abelian p -group A . The following two dual results are proved: ( * ) If A / G is countable and G is an almost totally projective group, then A is an almost totally projective group. ( * * ) If G is countable and nice in A such that A / G is an almost totally projective group, then A is an almost totally projective group. These results somewhat strengthen theorems due to Wallace (J. Algebra, 1971) and Hill (Comment. Math. Univ. Carol., 1995), respectively.

On localizations of torsion abelian groups

José L. Rodríguez, Jérôme Scherer, Lutz Strüngmann (2004)

Fundamenta Mathematicae

As is well known, torsion abelian groups are not preserved by localization functors. However, Libman proved that the cardinality of LT is bounded by | T | whenever T is torsion abelian and L is a localization functor. In this paper we study localizations of torsion abelian groups and investigate new examples. In particular we prove that the structure of LT is determined by the structure of the localization of the primary components of T in many cases. Furthermore, we completely characterize the relationship...

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