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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2019, Volume 105, Issue 3, Pages 421–427 (Mi mz11894)

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

T. A. Pushkovaa, A. M. Sebel'dinb

a Nizhny Novgorod State University of Architecture and Civil Engineering
b Nizhny Novgorod

Abstract: Let $C$ be an Abelian group. A class $X$ of Abelian groups is called a $_CE^\bullet H$-class if, for every groups $A,B\in X$, the isomorphisms $E^\bullet(A)\cong E^\bullet(B)$ and $\operatorname{Hom}(C,A)\cong\operatorname{Hom}(C,B)$ imply the isomorphism $A\cong B$.
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 groups is a $_CE^\bullet H$-class.

Keywords: completely decomposable Abelian group, homomorphism group, endomorphism semigroup, definability of Abelian groups.

DOI: https://doi.org/10.4213/mzm11894

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Document Type: Article
UDC: 512.541
Revised: 19.03.2018

Citation: T. A. Pushkova, A. M. Sebel'din, “Definability of Completely Decomposable Torsion-Free Abelian Groups by Endomorphism Semigroups and Homomorphism Groups”, Mat. Zametki, 105:3 (2019), 421–427

Citation in format AMSBIB
\Bibitem{PusSeb19} \by T.~A.~Pushkova, A.~M.~Sebel'din \paper Definability of Completely Decomposable Torsion-Free Abelian Groups by Endomorphism Semigroups and Homomorphism Groups \jour Mat. Zametki \yr 2019 \vol 105 \issue 3 \pages 421--427 \mathnet{http://mi.mathnet.ru/mz11894} \crossref{https://doi.org/10.4213/mzm11894} \elib{http://elibrary.ru/item.asp?id=37045128}