Geodesic
Nice Bases for Mixed and Torsion-free Abelian Groups
Bulletin of the Malaysian Mathematical Society, Tome 33 (2010) no. 3
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We prove that the divisible Abelian groups and the global Warfield Abelian groups have a nice basis, that is, they can be represented as a countable ascending union of nice direct sums of cyclic groups. We also show that there exists a mixed Abelian group which does not possess a nice basis as well as we find an unbounded reduced algebraically compact Abelian group which does not satisfy a stronger property. Some related concepts and questions are also considered. This continues our recent investigations in the torsion case published in (Atti Sem. Mat. Fis. Univ. Modena,
Classification : 20K10, 20K15, 20K21. 
@article{BMMS_2010_33_3_a4,
     author = {Peter Danchev},
     title = {Nice {Bases} for {Mixed} and {Torsion-free} {Abelian} {Groups}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2010},
     volume = {33},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2010_33_3_a4/}
}
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Peter Danchev. Nice Bases for Mixed and Torsion-free Abelian Groups. Bulletin of the Malaysian Mathematical Society, Tome 33 (2010) no. 3. http://geodesic.mathdoc.fr/item/BMMS_2010_33_3_a4/