This article is cited in 1 paper

Abelian groups with annihilator ideals of endomorphism rings

A. R. Chekhlov

Tomsk State University, Tomsk, Russia

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.

Keywords: nilpotent endomorphism, annihilator, principal ideal, self-injective endomorphism ring, almost injective group.

UDC: 512.541

MSC: 35R30

Received: 15.05.2017

DOI: 10.17377/smzh.2018.59.219

 English version: Siberian Mathematical Journal, 2018, 59:2, 363–367

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