Mediterranean Journal of Mathematics

, Volume 9, Issue 2, pp 295–304 | Cite as

On Cellular Covers with Free Kernels

Article

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.

Mathematics Subject Classification (2010)

Primary: 20K20 20K30 Secondary: 16S60 16W20 

Keywords

Cellular cover co-localization cotorsion-free free abelian group 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.’Area de Geometría y Topología, Facultad de Ciencias ExperimentalesUniversity of AlmeríaAlmeríaSpain
  2. 2.Department of MathematicsUniversity of Duisburg-EssenEssenGermany

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