Abelian Groups with Annihilator Ideals of Endomorphism Rings
- Authors: Chekhlov A.R.1
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Affiliations:
- Tomsk State University
- Issue: Vol 59, No 2 (2018)
- Pages: 363-367
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171826
- DOI: https://doi.org/10.1134/S0037446618020192
- ID: 171826
Cite item
Abstract
We describe the periodic groups whose endomorphism rings satisfy the annihilator condition for the principal left ideals generated by nilpotent elements. We prove that torsion-free reduced separable, vector, and algebraically compact groups have endomorphism rings with the annihilator condition for the principal left (right) ideals generated by nilpotent elements if and only if these rings are commutative. We show that the almost injective groups (in the sense of Harada) are injective, i.e. divisible.
About the authors
A. R. Chekhlov
Tomsk State University
Author for correspondence.
Email: cheklov@math.tsu.ru
Russian Federation, Tomsk
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