On Cellular Covers with Free Kernels
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
KeywordsCellular cover co-localization cotorsion-free free abelian group
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