二阶无扭零环的分类

IF 0.4 4区数学 Q4 MATHEMATICS

Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2023-09-30 DOI:10.36045/j.bbms.221123

Ryszard R. Andruszkiewicz, Mateusz Woronowicz

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引用次数: 0

摘要

本文给出了具有可分解的二阶无扭转加性群的零环的完全分类和具有不可分解的二阶无扭转加性群的零环的描述。进一步证明了二阶不可分解非零无扭阿贝尔群$A$只支持幂零环，当$A$是零环的加性群时。给出了二类无扭阿贝尔群的分解准则。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the Classification of Torsion-Free Nil Rings of Rank Two

The paper contains the complete classification of nil rings with decomposable torsion-free additive group of rank two and description of nil rings with indecomposable torsion-free additive group of rank two. Moreover, it is shown that an indecomposable non-nil torsion-free abelian group $A$ of rank two supports only nilpotent rings exactly if $A$ is the additive group of a nil ring. Some decomposition criteria for torsion-free abelian groups of rank two are also included.

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来源期刊

Bulletin of the Belgian Mathematical Society-Simon Stevin 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Bulletin of the Belgian Mathematical Society - Simon Stevin (BBMS) is a peer-reviewed journal devoted to recent developments in all areas in pure and applied mathematics. It is published as one yearly volume, containing five issues. The main focus lies on high level original research papers. They should aim to a broader mathematical audience in the sense that a well-written introduction is attractive to mathematicians outside the circle of experts in the subject, bringing motivation, background information, history and philosophy. The content has to be substantial enough: short one-small-result papers will not be taken into account in general, unless there are some particular arguments motivating publication, like an original point of view, a new short proof of a famous result etc. The BBMS also publishes expository papers that bring the state of the art of a current mainstream topic in mathematics. Here it is even more important that at leat a substantial part of the paper is accessible to a broader audience of mathematicians. The BBMS publishes papers in English, Dutch, French and German. All papers should have an abstract in English.