The hull-kernel topology on prime ideals in ordered semigroups

IF 1 4区数学 Q1 MATHEMATICS

Open Mathematics Pub Date : 2024-08-23 DOI:10.1515/math-2024-0050

Huanrong Wu, Huarong Zhang

{"title":"The hull-kernel topology on prime ideals in ordered semigroups","authors":"Huanrong Wu, Huarong Zhang","doi":"10.1515/math-2024-0050","DOIUrl":null,"url":null,"abstract":"The aim of this study is to develop the theory of prime ideals in ordered semigroups. First, to ensure the existence of prime ideals, we study a class of ordered semigroups which will be denoted by <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi mathvariant=\"double-struck\">S</m:mi> </m:mrow> <m:mrow> <m:mi>I</m:mi> <m:mi>P</m:mi> </m:mrow> </m:msub> </m:math> {{\\mathbb{S}}}_{IP} . And then we introduce the hull-kernel topology for the prime ideals <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">P</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>S</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {\\mathcal{P}}\\left(S) and the topological properties like separation axioms, compactness and connectedness are studied. Finally, we focus on the subspace <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">ℳ</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>S</m:mi> <m:mo>,</m:mo> <m:mi>I</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {\\mathcal{ {\\mathcal M} }}\\left(S,I) , minimal prime ideals containing the ideal <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>I</m:mi> </m:math> I in an ordered semigroup <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>S</m:mi> </m:math> S . We investigate topological properties of this subspace and connections between this subspace and the ordered semigroup <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>S</m:mi> </m:math> S .","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":"51 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Open Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/math-2024-0050","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

Abstract

The aim of this study is to develop the theory of prime ideals in ordered semigroups. First, to ensure the existence of prime ideals, we study a class of ordered semigroups which will be denoted by

S I P

{{\mathbb{S}}}_{IP}

. And then we introduce the hull-kernel topology for the prime ideals

P ( S )

{\mathcal{P}}\left(S)

and the topological properties like separation axioms, compactness and connectedness are studied. Finally, we focus on the subspace

ℳ ( S , I )

{\mathcal{ {\mathcal M} }}\left(S,I)

, minimal prime ideals containing the ideal

in an ordered semigroup

. We investigate topological properties of this subspace and connections between this subspace and the ordered semigroup

查看原文本刊更多论文

有序半群质心的赫尔核拓扑学

本研究旨在发展有序半群中的素理想理论。首先，为了确保素理想的存在，我们研究了一类有序半群，用 S I P {{\mathbb{S}}{{IP} 表示。然后，我们引入素理想 P ( S ) {\mathcal{P}}\left(S) 的赫尔核拓扑，并研究分离公理、紧凑性和连通性等拓扑性质。最后，我们聚焦于子空间ℳ ( S , I ) {\mathcal{ {\mathcal M}}\left(S,I)}}left(S,I)，包含有序半群 S S 中理想 I I 的最小素理想。我们研究这个子空间的拓扑性质以及这个子空间与有序半群 S S 之间的联系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Open Mathematics MATHEMATICS-

CiteScore

2.40

自引率

5.90%

发文量

审稿时长

16 weeks

期刊介绍： Open Mathematics - formerly Central European Journal of Mathematics Open Mathematics is a fully peer-reviewed, open access, electronic journal that publishes significant, original and relevant works in all areas of mathematics. The journal provides the readers with free, instant, and permanent access to all content worldwide; and the authors with extensive promotion of published articles, long-time preservation, language-correction services, no space constraints and immediate publication. Open Mathematics is listed in Thomson Reuters - Current Contents/Physical, Chemical and Earth Sciences. Our standard policy requires each paper to be reviewed by at least two Referees and the peer-review process is single-blind. Aims and Scope The journal aims at presenting high-impact and relevant research on topics across the full span of mathematics. Coverage includes: