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- W4300792166 abstract "Recall that a homomorphism of $R$-modules $pi: Gto H$ is called a {it cellular cover} over $H$ if $pi$ induces an isomorphism $pi_*: Hom_R(G,G)cong Hom_R(G,H),$ where $pi_*(varphi)= pi varphi$ for each $varphi in Hom_R(G,G)$ (where maps are acting on the left). In this paper we show that every cotorsion-free module $K$ of finite rank can be realized as the kernel of a cellular cover of some cotorsion-free module of rank 2. In particular, every free abelian group of any finite rank appears then as the kernel of a cellular cover of a cotorsion-free abelian group of rank 2. This situation is 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 comes motivated by an example due to Buckner and Dugas, and recent results obtained by Gobel--Rodr'iguez--Strungmann, and Fuchs--Gobel." @default.
- W4300792166 created "2022-10-04" @default.
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- W4300792166 date "2010-01-14" @default.
- W4300792166 modified "2023-10-18" @default.
- W4300792166 title "On cellular covers with free kernels" @default.
- W4300792166 doi "https://doi.org/10.48550/arxiv.1001.2457" @default.
- W4300792166 hasPublicationYear "2010" @default.
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