On radicals and products
Copyright policy )On radicals and products
An abelian group G is called cotorsion-free if G is torsion-free, reduced and, for each prime p, G does not contain a copy of the p-adic integers. The authors construct, for every cotorsion-free group G, a slender, \(\aleph_ 1\)-free abelian group A such that \(Hom(A,G)=0\). This is used to solve some open problems on radicals and torsion theories of abelian groups.
Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups, slender, \(\aleph _ 1\)-free abelian group, 20K20, Subgroups of abelian groups, torsion theories of abelian groups, 16A63, Torsion-free groups, infinite rank, radicals, cotorsion-free group
Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups, slender, \(\aleph _ 1\)-free abelian group, 20K20, Subgroups of abelian groups, torsion theories of abelian groups, 16A63, Torsion-free groups, infinite rank, radicals, cotorsion-free group
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