Abelian RE-Groups

被引：0

作者：

Kolenova, E. M. ^{[1
]}

Pushkova, T. A. ^{[2
]}

机构：

[1] Nizhny Novgorod State Pedag Univ, Nizhnii Novgorod 603950, Russia

[2] Nizhny Novgorod State Univ Architecture & Civil E, Nizhnii Novgorod 603950, Russia

来源：

MATHEMATICAL NOTES | 2020年 / 107卷 / 3-4期

关键词：

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;

D O I：

10.1134/S0001434620030268

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：595 / 599

页数：5