Torsion-Free Weakly Transitive E-Engel Abelian Groups

A. R. Chekhlov

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Torsion-Free Weakly Transitive E-Engel Abelian Groups

机译：无扭转弱传递E-Engel阿贝尔群

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摘要

It is proved that if all the endomorphisms of a reduced torsion-free weakly transitive Abelian group are bounded right-nilpotent, then its ring of endomorphisms is commutative. The ring of endomorphisms of a torsion-free Abelian group with periodic group of automorphisms and Engel ring of endomorphisms is also commutative.

机译：证明了，如果减少了无扭转的弱传递阿贝尔群的所有内同态都是有界的右幂零，那么它的内同态环是可交换的。具有周期自同构群的无扭转阿贝尔群的内同形环和内同形的恩格尔环也是可交换的。

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来源
《Mathematical notes》 |2013年第4期|583-589|共7页
作者
A. R. Chekhlov;
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作者单位

Tomsk State University, Tomsk, Russia;

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原文格式 PDF
正文语种 eng
中图分类
关键词
E-Engel Abelian group; weakly transitive group; torsion-free Abelian group; ring of endomorphisms; periodic group of automorphisms; n-step Engel ring; Lie algebra; E-nilpotent group; nilpotent element of a ring;

机译：E-Engel Abelian小组;弱传递群无扭转的阿贝尔群;同态环自同构的周期性群n步恩格尔环;李代数电子无能组;环的幂等元素;

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专利

1. RATIONAL RINGS RELATED TO WEAKLY TRANSITIVE TORSION-FREE ABELIAN GROUPS [J] . Meehan C, Strungmann L Journal of algebra and its applications . 2009,第5期

机译：与弱传递扭转无阿贝尔群相关的有理环
2. Torsion-free weakly transitive abelian groups [J] . Goldsmith B, Strungmann L Communications in algebra . 2005,第4期

机译：无扭转的弱传递阿贝尔群
3. On commutator Krylov transitive and commutator weakly transitive Abelian p-groups [J] . Chekhlov Andrey R., Danchev Peter V Forum mathematicum . 2019,第6期

机译：在换向器Krylov传递和换向器弱异步abelian p组
4. 0"-Categorical Completely Decomposable Torsion-Free Abelian Groups [C] . Alexander G. Melnikov Mathematical theory and computational practice . 2009

机译：0 “-分类完全可分解的无扭转阿贝尔群
5. Graphs on which dihedral, quaternion, and abelian groups act vertex and/or edge transitively and applications to tensor products [D] . Sanders, Robin Sue. 1990

机译：二面，四元数和阿贝尔群在其顶点和/或边上传递性作用的图形以及在张量积上的应用
6. Generalized Weak Transitivity of Preference [O] . Thomas A. Runkler -1

机译：偏好的广义弱传递性
7. Uniquely Transitive Torsion-free Abelian Groups [O] . Göbel, Rüdiger, Shelah, Saharon 2004

机译：独特的传递无扭转阿贝尔群

Torsion-Free Weakly Transitive E-Engel Abelian Groups

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