This article is cited in 1 paper

On definability of completely decomposable torsion-free Abelian groups by certain groups of homomorphisms

T. A. Beregovaya

Chair of Mathematics, Nizhni Novgorod Architecture and Building University, Nizhni Novgorod, Russia

Abstract: Let $C$ be an Abelian group. An Abelian group $A$ in some class $X$ of Abelian groups is said to be $_CH$-definable in the class $X$ if for any group $B\in X$ the isomorphism $\mathrm{Hom}(C,A)\cong\mathrm{Hom}(C,B)$ implies that $A\cong B$. If every group in $X$ is $_CH$-definable in $X$, then the class $X$ is called a $_CH$-class. In this paper we study conditions that make a class of completely decomposable torsion-free Abelian groups a $_CH$-class, where $C$ is a vector group.

Keywords: completely decomposable torsion-free Abelian group, vector Abelian group, group of homomorphisms, definability of Abelian groups.

UDC: 512.541

Received: 31.08.2007

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2009, 53:11, 16–19

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