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–Gobel, and Gobel–Rodriguez–Strungmann.
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