Geodesic
Abelian RE-Groups
Matematičeskie zametki, Tome 107 (2020) no. 4, pp. 533-538

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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, periodic group, unreduced group, torsion-free rank-1 group, endomorphism group of an Abelian group, endomorphism ring of an Abelian group.
Mots-clés : $E^+$-group, divisible group 
@article{MZM_2020_107_4_a3,
     author = {E. M. Kolenova and T. A. Pushkova},
     title = {Abelian {RE-Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {533--538},
     publisher = {mathdoc},
     volume = {107},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_4_a3/}
}
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E. M. Kolenova; T. A. Pushkova. Abelian RE-Groups. Matematičeskie zametki, Tome 107 (2020) no. 4, pp. 533-538. http://geodesic.mathdoc.fr/item/MZM_2020_107_4_a3/