Definability of Completely Decomposable Torsion-Free Abelian Groups by Endomorphism Semigroups and Homomorphism Groups
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Let C be an Abelian group. A class X of Abelian groups is called a CE•H-class if, for every groups A, B ∈ X, the isomorphisms E•(A) ≅ E•(B) and Hom(C, A) ≅ Hom(C, B) imply the isomorphism A ≅ B. In the paper, necessary and sufficient conditions on a completely decomposable torsion-free Abelian group C are described under which a given class of torsion-free Abelian groupsisa CE•H-class.
Keywordscompletely decomposable Abelian group homomorphism group endomorphism semigroup definability of Abelian groups
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