hx - group和hypergroup之间的链路

IF 0.4 4区数学 Q4 MATHEMATICS

Algebra Colloquium Pub Date : 2021-09-01 DOI:10.1142/s1005386721000341

I. Cristea, M. Novák, B. Onasanya

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引用次数: 2

摘要

群的概念是对群概念的升级，在群的非空子集族上定义了一个新的运算。如果这个新的支持集和新的操作是一个组，那么我们称它为[公式:见文本]-组。另一方面，超运算是一种映射，它与一个[公式:见文本]群的运算具有相同的上域，即初始集合的非空子集族，但具有不同的域-集合本身。这可能是(而且确实是)混淆的根源，本文对此进行了澄清。此外，[公式:见文本]群自然导致超群的构造。提出了这两个代数概念之间的联系，目的是在当前代数超结构的研究中复兴一个[公式:见文本]群的旧概念。并对其中一个现有环节和一个新建立的环节进行了讨论。

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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Links Between HX-Groups and Hypergroups

The concept of an [Formula: see text]-group is an upgrade of the concept of a group, in which a new operation is defined on the family of non-empty subsets of a group. If this new support set together with the new operation is a group, then we call it an [Formula: see text]-group. On the other hand, a hyperoperation is a mapping having the same codomain as the operation of an [Formula: see text]-group, i.e., the family of non-empty subsets of the initial set, but a different domain — the set itself. This could be (and was indeed) a source of confusion, which is clarified in this paper. Moreover, [Formula: see text]-groups naturally lead to constructions of hypergroups. The links between these two algebraic concepts are presented, with the aim of reviving the old notion of an [Formula: see text]-group in the current research on algebraic hyperstructures. One of such existing links and one newly established link are also discussed.

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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.