Geodesic
Definability of Completely Decomposable Torsion-Free Abelian Groups by Endomorphism Semigroups and Homomorphism Groups
Matematičeskie zametki, Tome 105 (2019) no. 3, pp. 421-427.

Voir la notice de l'article provenant de la source Math-Net.Ru

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, endomorphism semigroup, definability of Abelian groups.
Mots-clés : homomorphism group 
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     title = {Definability of {Completely} {Decomposable} {Torsion-Free} {Abelian} {Groups} by {Endomorphism} {Semigroups} and {Homomorphism} {Groups}},
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T. A. Pushkova; A. M. Sebel'din. Definability of Completely Decomposable Torsion-Free Abelian Groups by Endomorphism Semigroups and Homomorphism Groups. Matematičeskie zametki, Tome 105 (2019) no. 3, pp. 421-427. http://geodesic.mathdoc.fr/item/MZM_2019_105_3_a8/

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