无扭转ti群的分类

IF 0.4 4区数学 Q4 MATHEMATICS

Algebra Colloquium Pub Date : 2022-12-01 DOI:10.1142/s1005386722000414

R. Andruszkiewicz, M. Woronowicz

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引用次数: 0

摘要

如果与加性群(公式:见文)相结合的每个环都是子环，则一个阿贝尔群(公式:见文)称为[公式:见文]群。环[公式:见文]的亲缘性意味着环[公式:见文]是结合的，并且[公式:见文]的任何理想的所有理想都是[公式:见文]中的理想。本文描述了无扭[公式:见文]-群直至结合型零群的结构。还证明了，对于非关联零的无扭阿贝尔群，条件[公式:见文]暗示了不可分解性和齐性。本文包含了[公式:见文]从2到[公式:见文]的任意秩的对非同构群的构造。

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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The Classification of Torsion-free TI-Groups

An abelian group [Formula: see text] is called a [Formula: see text]-group if every associative ring with the additive group [Formula: see text] is filial. The filiality of a ring [Formula: see text] means that the ring [Formula: see text] is associative and all ideals of any ideal of [Formula: see text] are ideals in [Formula: see text]. In this paper, torsion-free [Formula: see text]-groups are described up to the structure of associative nil groups. It is also proved that, for torsion-free abelian groups that are not associative nil, the condition [Formula: see text] implies the indecomposability and homogeneity. The paper contains constructions of [Formula: see text] such groups of any rank from 2 to[Formula: see text] which are pairwise non-isomorphic.

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来源期刊

Algebra Colloquium 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

625

审稿时长

15.6 months

期刊介绍： Algebra Colloquium is an international mathematical journal founded at the beginning of 1994. It is edited by the Academy of Mathematics & Systems Science, Chinese Academy of Sciences, jointly with Suzhou University, and published quarterly in English in every March, June, September and December. Algebra Colloquium carries original research articles of high level in the field of pure and applied algebra. Papers from related areas which have applications to algebra are also considered for publication. This journal aims to reflect the latest developments in algebra and promote international academic exchanges.