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.
Keywords:Abelian group, $E^+$-group, periodic group, divisible group, unreduced group, torsion-free rank-1 group, endomorphism group of an Abelian group, endomorphism ring of an Abelian group.
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