On Fully Idempotent Homomorphisms of Abelian Groups


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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.

About the authors

A. R. Chekhlov

Tomsk State University

Author for correspondence.
Email: cheklov@math.tsu.ru
Russian Federation, Tomsk

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