On Fully Idempotent Homomorphisms of Abelian Groups
- Authors: Chekhlov A.R.1
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Affiliations:
- Tomsk State University
- Issue: Vol 60, No 4 (2019)
- Pages: 727-733
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172583
- DOI: https://doi.org/10.1134/S0037446619040189
- ID: 172583
Cite item
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