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.
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Russian Text © The Author(s), 2019, published in Sibirskii Matematicheskii Zhurnal, 2019, Vol. 60, No. 4, pp. 932–940.
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Chekhlov, A.R. On Fully Idempotent Homomorphisms of Abelian Groups. Sib Math J 60, 727–733 (2019). https://doi.org/10.1134/S0037446619040189
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DOI: https://doi.org/10.1134/S0037446619040189