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Sibirskii Matematicheskii Zhurnal, 2019, Volume 60, Number 4, Pages 932–940
DOI: https://doi.org/10.33048/smzh.2019.60.418
(Mi smj3126)
 

On fully idempotent homomorphisms of abelian groups

A. R. Chekhlov

Tomsk State University, Tomsk, Russia
References:
Abstract: We provide some examples of irregular fully idempotent homomorphisms and study the pairs of abelian groups $A$ and $B$ for which the homomorphism group $\operatorname{Hom}(A,B)$ is fully idempotent. We show that if $B$ is a torsion group or a mixed split group and if at least one of the groups $A$ or $B$ is divisible then the full idempotence of the homomorphism group implies its regularity. If at least one of the groups $A$ or $B$ is a reduced torsion-free group and their homomorphism groups are nonzero then the group is not fully idempotent. The study of fully idempotent groups $\operatorname{Hom}(A,A)$ comes down to reduced mixed groups $A$ with dense elementary torsion part.
Keywords: regular homomorphism, fully idempotent homomorphism, homomorphism group, mixed group, self-small group.
Received: 04.09.2018
Revised: 04.09.2018
Accepted: 19.12.2018
English version:
Siberian Mathematical Journal, 2019, Volume 60, Issue 4, Pages 727–733
DOI: https://doi.org/10.1134/S0037446619040189
Bibliographic databases:
Document Type: Article
UDC: 512.541
Language: Russian
Citation: A. R. Chekhlov, “On fully idempotent homomorphisms of abelian groups”, Sibirsk. Mat. Zh., 60:4 (2019), 932–940; Siberian Math. J., 60:4 (2019), 727–733
Citation in format AMSBIB
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\paper On fully idempotent homomorphisms of abelian groups
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\vol 60
\issue 4
\pages 932--940
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\crossref{https://doi.org/10.33048/smzh.2019.60.418}
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\jour Siberian Math. J.
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\vol 60
\issue 4
\pages 727--733
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