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Siberian Mathematical Journal

, Volume 60, Issue 4, pp 727–733 | Cite as

On Fully Idempotent Homomorphisms of Abelian Groups

  • A. R. ChekhlovEmail author
Article
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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 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 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 

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© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.Tomsk State UniversityTomskRussia

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