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This article is cited in 3 scientific papers (total in 3 papers)
Definability of Completely Decomposable Torsion-Free Abelian Groups by Groups of Homomorphisms
T. A. Beregovaya, A. M. Sebel'din Nizhny Novgorod State Pedagogical University
Abstract:
Let $C$ be an Abelian group. An Abelian group $A$ in some class $\mathscr X$ of Abelian groups is said to be $\sideset{_C}{}{\mathop H}$-definable in the class $\mathscr X$ if, for any group $B\in\mathscr X$, it follows from the existence of an isomorphism $\operatorname{Hom}(C,A)\cong\operatorname{Hom}(C,B)$ that there is an isomorphism $A\cong B$. If every group in $\mathscr X$ is ${}_CH$-definable in $\mathscr X$, then the class $\mathscr X$ is called an ${}_CH$-class. In the paper, conditions are studied under which a class of completely decomposable torsion-free Abelian groups is a $\sideset{_C}{}{\mathop H}$-class, where $C$ is a completely decomposable torsion-free Abelian group.
Received: 04.09.2001
Citation:
T. A. Beregovaya, A. M. Sebel'din, “Definability of Completely Decomposable Torsion-Free Abelian Groups by Groups of Homomorphisms”, Mat. Zametki, 73:5 (2003), 643–648; Math. Notes, 73:5 (2003), 605–610
Linking options:
https://www.mathnet.ru/eng/mzm212https://doi.org/10.4213/mzm212 https://www.mathnet.ru/eng/mzm/v73/i5/p643
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Abstract page: | 365 | Full-text PDF : | 202 | References: | 58 | First page: | 1 |
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