Abstract
An Abelian group on which every nonzero ring is isomorphic to the ring of endomorphisms of this group is called an RE-group. In the present paper, the RE-groups are described in some classes of Abelian groups, including periodic, divisible, unreduced, and torsion-free rank-1 groups. It is shown that there are no RE-groups in the class of completely decomposable torsion-free Abelian groups.
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A. M. Sebel’din, “On groups of homomorphisms of Abelian torsion-free groups,” in Abelian Groups and Modules (Izd. Tomsk. Univ., Tomsk, 1976), pp. 78–86 [in Russian].
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Russian Text © The Author(s), 2020, published in Matematicheskie Zametki, 2020, Vol. 107, No. 4, pp. 533–538.
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Kolenova, E.M., Pushkova, T.A. Abelian RE-Groups. Math Notes 107, 595–599 (2020). https://doi.org/10.1134/S0001434620030268
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DOI: https://doi.org/10.1134/S0001434620030268