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Fundam. Prikl. Mat., 2019, Volume 22, Issue 5, Pages 145–152 (Mi fpm1843)  

Definability of completely decomposable torsion-free Abelian groups by semigroups of endomorphism and groups of homomorphisms

T. A. Pushkova

Nizhny Novgorod State University of Architecture and Civil Engineering

Abstract: Let $C $ be an Abelian group. A class $X $ of Abelian groups is called a $_CE ^\bullet H $-class if for any groups $A,B \in X$, it follows from the existence of isomorphisms $E^\bullet (A) \cong E^\bullet (B)$ and $\operatorname{Hom}(C,A)\cong \operatorname{Hom}(C,B) $ that there is an isomorphism $A\cong B $. In this paper, conditions are studied under which the class $\Im _{\mathrm{cd}}^{\mathrm{ad}}$ of completely decomposable almost divisible Abelian groups and class $ \Im _{\mathrm{cd}}^{*} $ of completely decomposable torsion-free Abelian groups $A$ where $\Omega(A)$ contains only incomparable types are $_CE ^\bullet H $-classes, where $C $ is a completely decomposable torsion-free Abelian group.

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UDC: 512.541

Citation: T. A. Pushkova, “Definability of completely decomposable torsion-free Abelian groups by semigroups of endomorphism and groups of homomorphisms”, Fundam. Prikl. Mat., 22:5 (2019), 145–152

Citation in format AMSBIB
\Bibitem{Pus19}
\by T.~A.~Pushkova
\paper Definability of completely decomposable torsion-free
Abelian groups by semigroups of endomorphism and groups of homomorphisms
\jour Fundam. Prikl. Mat.
\yr 2019
\vol 22
\issue 5
\pages 145--152
\mathnet{http://mi.mathnet.ru/fpm1843}


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