e -析取逆半群

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-09-17 DOI:10.1016/j.jalgebra.2025.08.041

Luna Elliott , Alex Levine , James Mitchell

{"title":"e -析取逆半群","authors":"Luna Elliott , Alex Levine , James Mitchell","doi":"10.1016/j.jalgebra.2025.08.041","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper we provide an overview of the class of inverse semigroups <em>S</em> such that every non-trivial congruence on <em>S</em> relates at least one idempotent to a non-idempotent; such inverse semigroups are called <em>E-disjunctive</em>. This overview includes the study of the inverse semigroup theoretic structure of <em>E</em>-disjunctive semigroups; a large number of natural examples; some asymptotic results establishing the rarity of such inverse semigroups; and a general structure theorem for all inverse semigroups where the building blocks are <em>E</em>-disjunctive.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"687 ","pages":"Pages 292-344"},"PeriodicalIF":0.8000,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"E-disjunctive inverse semigroups\",\"authors\":\"Luna Elliott , Alex Levine , James Mitchell\",\"doi\":\"10.1016/j.jalgebra.2025.08.041\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper we provide an overview of the class of inverse semigroups <em>S</em> such that every non-trivial congruence on <em>S</em> relates at least one idempotent to a non-idempotent; such inverse semigroups are called <em>E-disjunctive</em>. This overview includes the study of the inverse semigroup theoretic structure of <em>E</em>-disjunctive semigroups; a large number of natural examples; some asymptotic results establishing the rarity of such inverse semigroups; and a general structure theorem for all inverse semigroups where the building blocks are <em>E</em>-disjunctive.</div></div>\",\"PeriodicalId\":14888,\"journal\":{\"name\":\"Journal of Algebra\",\"volume\":\"687 \",\"pages\":\"Pages 292-344\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2025-09-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021869325005277\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021869325005277","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们概述了一类逆半群S，使得S上的每一个非平凡同余至少有一个幂等与一个非幂等相关；这样的逆半群称为e -析取的。本文综述了e -析取半群的逆半群理论结构的研究；大量的自然例子；建立这类逆半群的稀有性的一些渐近结果以及构造块为e析取的所有逆半群的一般结构定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

E-disjunctive inverse semigroups

In this paper we provide an overview of the class of inverse semigroups S such that every non-trivial congruence on S relates at least one idempotent to a non-idempotent; such inverse semigroups are called E-disjunctive. This overview includes the study of the inverse semigroup theoretic structure of E-disjunctive semigroups; a large number of natural examples; some asymptotic results establishing the rarity of such inverse semigroups; and a general structure theorem for all inverse semigroups where the building blocks are E-disjunctive.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.