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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阿贝尔 RE 群

每个非零环都与该群的自同态环同构的阿贝尔群称为 RE-群。在本文中，RE 群在一些阿贝尔群中进行了描述，包括周期群、可分群、未约化和无扭 1 阶群。结果表明，在完全可分解无扭阿贝尔群的类中不存在RE群。