|
This article is cited in 1 scientific paper (total 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.
Received: 15.05.2017
Citation:
A. R. Chekhlov, “Abelian groups with annihilator ideals of endomorphism rings”, Sibirsk. Mat. Zh., 59:2 (2018), 461–467; Siberian Math. J., 59:2 (2018), 363–367
Linking options:
https://www.mathnet.ru/eng/smj2986 https://www.mathnet.ru/eng/smj/v59/i2/p461
|
|