Definability of Completely Decomposable Torsion-Free Abelian Groups by Endomorphism Semigroups and Homomorphism Groups

摘要

Let C be an Abelian group. A class X of Abelian groups is called a (CEH)-H-center dot-class if, for every groups A, B X, the isomorphisms E-center dot(A) E-center dot(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 (CEH)-H-center dot-class.