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Mathematical Notes

, Volume 105, Issue 3–4, pp 398–403 | Cite as

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

  • T. A. PushkovaEmail author
  • A. M. Sebel’dinEmail author
Article
  • 12 Downloads

Abstract

Let C be an Abelian group. A class X of Abelian groups is called a CEH-class if, for every groups A, BX, the isomorphisms E(A) ≅ E(B) and Hom(C, A) ≅ Hom(C, B) imply the isomorphism AB. 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-class.

Keywords

completely decomposable Abelian group homomorphism group endomorphism semigroup definability of Abelian groups 

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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Nizhny Novgorod State University of Architecture and Civil EngineeringNizhny NovgorodRussia
  2. 2.“Mathematical Notes,” Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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