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Matematicheskie Zametki, 2020, Volume 107, Issue 4, Pages 533–538
DOI: https://doi.org/10.4213/mzm12318 (Mi mzm12318) 		 
Abelian RE-Groups

E. M. Kolenovaa, T. A. Pushkovab

a Nizhny Novgorod State Pedagogical University
b Nizhny Novgorod State University of Architecture and Civil Engineering
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DOI: https://doi.org/10.4213/mzm12318
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.
Received: 21.01.2019
Revised: 27.05.2019
English version:
Mathematical Notes, 2020, Volume 107, Issue 4, Pages 595–599
DOI: https://doi.org/10.1134/S0001434620030268
Bibliographic databases:
Document Type: Article
UDC: 512.541
Language: Russian
Citation: E. M. Kolenova, T. A. Pushkova, “Abelian RE-Groups”, Mat. Zametki, 107:4 (2020), 533–538; Math. Notes, 107:4 (2020), 595–599
Citation in format AMSBIB
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