变换半群中的放大镜，其限制属于给定半群

IF 0.5 Q3 MATHEMATICS

Asian-European Journal of Mathematics Pub Date : 2023-11-08 DOI:10.1142/s1793557123502273

Sushree Khirabdhi, Shubh N. Singh

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引用次数: 0

摘要

设[公式:见文]为集合[公式:见文]上的全变换半群。对于[公式:见文]的子集[公式:见文]和[公式:见文]的子群[公式:见文]，用[公式:见文]表示由所有变换[公式:见文]组成的复合半群，使得[公式:见文]对[公式:见文]的限制[公式:见文]属于[公式:见文]。给出了[公式:见文]中元素为左或右放大镜的充分必要条件。我们应用这些描述得到了关于半群[公式:见文]和[公式:见文]的更具体的结果，其中[公式:见文](分别，[公式:见文])是由所有内射(分别，满射)变换组成的[公式:见文]的特定子群。这篇论文还指出了文献中出现的一些关于[公式:见文本]的结果。

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Magnifiers in semigroups of transformations whose restrictions belong to a given semigroup

Let [Formula: see text] be the full transformation semigroup on a set [Formula: see text]. For a subset [Formula: see text] of [Formula: see text] and a submonoid [Formula: see text] of [Formula: see text], denote by [Formula: see text] the semigroup under composition consisting of all transformations [Formula: see text] such that the restriction [Formula: see text] of [Formula: see text] to [Formula: see text] belongs to [Formula: see text]. We give necessary and sufficient conditions for an element in [Formula: see text] to be left or right magnifier. We apply these descriptions to obtain more concrete results for the semigroups [Formula: see text] and [Formula: see text], where [Formula: see text] (respectively, [Formula: see text]) is the specific submonoid of [Formula: see text] consisting of all injective (respectively, surjective) transformations. The paper also identifies some results on [Formula: see text] that have appeared in the literature.

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来源期刊

Asian-European Journal of Mathematics MATHEMATICS-

CiteScore

1.30

自引率

12.50%

发文量

169

期刊介绍： Asian-European Journal of Mathematics is an international journal which is devoted to original research in the field of pure and applied mathematics. The aim of the journal is to provide a medium by which new ideas can be discussed among researchers from diverse fields in mathematics. It publishes high quality research papers in the fields of contemporary pure and applied mathematics with a broad range of topics including algebra, analysis, topology, geometry, functional analysis, number theory, differential equations, operational research, combinatorics, theoretical statistics and probability, theoretical computer science and logic. Although the journal focuses on the original research articles, it also welcomes survey articles and short notes. All papers will be peer-reviewed within approximately four months.