Definability of Completely Decomposable Torsion-Free Abelian Groups by Endomorphism Semigroups and Homomorphism Groups
Tat'yana Aleksandrovna Pushkova, Анатолий Михайлович Себельдин · Mathematical Notes · 2019
Let C be an Abelian group. A class X of Abelian groups is called a C E • 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 C E • H -class.