From pre-trusses to skew braces

IF 0.8 3区数学 Q2 MATHEMATICS

Publicacions Matematiques Pub Date : 2020-07-11 DOI:10.5565/publmat6622206

Tomasz Brzezi'nski, Stefano Mereta, Bernard Rybołowicz

引用次数: 4

Abstract

The notion of a pre-truss, that is, a set that is both a heap and a semigroup is introduced. Pre-trusses themselves as well as pre-trusses in which one-sided or two-sided distributive laws hold are studied. These are termed near-trusses and skew trusses respectively. Congruences in pre-trusses are shown to correspond to paragons defined here as sub-heaps satisfying particular closure property. Near-trusses corresponding to skew braces and near-rings are identified through their paragon and ideal structures. Regular elements in a pre-truss are defined leading to the notion of a (pre-truss) domain. The latter are described as quotients by completely prime paragons, also defined hereby. Regular pre-trusses as domains that satisfy the Ore condition are introduced and the pre-trusses of fractions are defined. In particular, it is shown that near-trusses of fractions without an absorber correspond to skew braces.

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从预桁架到斜撑

引入了前桁架的概念，即既是堆又是半群的集合。研究了预桁架本身以及单侧或双侧分布律成立的预桁架。这些分别被称为近桁架和斜桁架。预桁架中的同余与此处定义为满足特定闭合性质的子堆的分段相对应。通过斜撑和近环的截面和理想结构识别出与斜撑和环相对应的近桁架。前桁架中的规则元素被定义为（前桁架）域的概念。后者被完全素数段描述为商，也在这里定义。引入了满足Ore条件的规则预桁架，并定义了分数预桁架。特别地，研究表明，没有吸收器的部分的近桁架对应于斜撑。

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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来源期刊

Publicacions Matematiques 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publicacions Matemàtiques is a research mathematical journal published by the Department of Mathematics of the Universitat Autònoma de Barcelona since 1976 (before 1988 named Publicacions de la Secció de Matemàtiques, ISSN: 0210-2978 print, 2014-4369 online). Two issues, constituting a single volume, are published each year. The journal has a large circulation being received by more than two hundred libraries all over the world. It is indexed by Mathematical Reviews, Zentralblatt Math., Science Citation Index, SciSearch®, ISI Alerting Services, COMPUMATH Citation Index®, and it participates in the Euclid Project and JSTOR. Free access is provided to all published papers through the web page. Publicacions Matemàtiques is a non-profit university journal which gives special attention to the authors during the whole editorial process. In 2019, the average time between the reception of a paper and its publication was twenty-two months, and the average time between the acceptance of a paper and its publication was fifteen months. The journal keeps on receiving a large number of submissions, so the authors should be warned that currently only articles with excellent reports can be accepted.