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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - E. M. Kolenova
AU  - T. A. Pushkova
TI  - Abelian RE-Groups
JO  - Matematičeskie zametki
PY  - 2020
SP  - 533
EP  - 538
VL  - 107
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2020_107_4_a3/
LA  - ru
ID  - MZM_2020_107_4_a3
ER  - 
%0 Journal Article
%A E. M. Kolenova
%A T. A. Pushkova
%T Abelian RE-Groups
%J Matematičeskie zametki
%D 2020
%P 533-538
%V 107
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2020_107_4_a3/
%G ru
%F MZM_2020_107_4_a3
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/

[1] L. Fuks, Beskonechnye abelevy gruppy, T. 2, Mir, M., 1977 | MR | Zbl

[2] E. M. Kolenova, A. M. Sebeldin, “Ob izomorfnosti abelevoi gruppy svoei gruppe endomorfizmov”, Matem. zametki, 80:4 (2006), 536–545 | DOI | MR | Zbl

[3] A. M. Sebeldin, “Gruppy gomomorfizmov vpolne razlozhimykh abelevykh grupp bez krucheniya”, Izv. vuzov. Matem., 1973, no. 7, 77–84 | MR | Zbl

[4] A. M. Sebeldin, “O gruppakh gomomorfizmov abelevykh grupp bez krucheniya”, Abelevy gruppy i moduli, Izd-vo Tomskogo un-ta, Tomsk, 1976, 78–86