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Abelian Groups with Annihilator Ideals of Endomorphism Rings

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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.

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Authors and Affiliations

  1. Tomsk State University, Tomsk, Russia

    A. R. Chekhlov

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  1. A. R. Chekhlov
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Correspondence to A. R. Chekhlov.

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Original Russian Text Copyright © 2018 Chekhlov A.R.

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Chekhlov, A.R. Abelian Groups with Annihilator Ideals of Endomorphism Rings. Sib Math J 59, 363–367 (2018). https://doi.org/10.1134/S0037446618020192

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  • DOI: https://doi.org/10.1134/S0037446618020192

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