Abstract
In this paper we show that every cotorsion-free and reduced abelian group of any finite rank (in particular, every free abelian group of finite rank) appears as the kernel of a cellular cover of some cotorsion-free abelian group of rank 2. This situation is the best possible in the sense that cotorsion-free abelian groups of rank 1 do not admit cellular covers with free kernel except for the trivial ones. This work is motivated by an example due to Buckner–Dugas, and recent results obtained by Fuchs–Göbel, and Göbel–Rodríguez–Strüngmann.
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The first author was supported by the Spanish Ministry of Education and Science MEC-FEDER grant MTM2007-63277, and Junta de Andalucía grants FQM-213 and P07-FQM-2863.
The second author was supported by the project No. 963-98.6/2007 of the German-Israeli Foundation for Scientific Research & Development.
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Rodríguez, J.L., Strüngmann, L. On Cellular Covers with Free Kernels. Mediterr. J. Math. 9, 295–304 (2012). https://doi.org/10.1007/s00009-010-0109-1
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DOI: https://doi.org/10.1007/s00009-010-0109-1