准连续完整半网格的定义方程和反射子类

IF 0.7 3区数学 Q2 MATHEMATICS Semigroup Forum Pub Date : 2024-07-26 DOI:10.1007/s00233-024-10459-1

Wei Luan, Qingguo Li

{"title":"准连续完整半网格的定义方程和反射子类","authors":"Wei Luan, Qingguo Li","doi":"10.1007/s00233-024-10459-1","DOIUrl":null,"url":null,"abstract":"<p>In 1981, Gerhard Gierz and Jimmie Lawson gave a necessary condition for a complete lattice to be quasicontinuous using an equation. However, whether quasicontinuous lattices can be characterized by equations has remained unknown. In this paper, we give an equational characterization of quasicontinuous complete semilattices. Furthermore, we investigate congruences of quasicontinuous complete semilattices. We derive the first isomorphism theorem for quasicontinuous complete semilattices in the context of C-congruences. As a consequence, we show that the category of all continuous complete semilattices with maps preserving directed sups and nonempty infs is a reflective full subcategory of quasicontinuous complete semilattices.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"11 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A defining equation and reflective subcategories of quasicontinuous complete semilattices\",\"authors\":\"Wei Luan, Qingguo Li\",\"doi\":\"10.1007/s00233-024-10459-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In 1981, Gerhard Gierz and Jimmie Lawson gave a necessary condition for a complete lattice to be quasicontinuous using an equation. However, whether quasicontinuous lattices can be characterized by equations has remained unknown. In this paper, we give an equational characterization of quasicontinuous complete semilattices. Furthermore, we investigate congruences of quasicontinuous complete semilattices. We derive the first isomorphism theorem for quasicontinuous complete semilattices in the context of C-congruences. As a consequence, we show that the category of all continuous complete semilattices with maps preserving directed sups and nonempty infs is a reflective full subcategory of quasicontinuous complete semilattices.</p>\",\"PeriodicalId\":49549,\"journal\":{\"name\":\"Semigroup Forum\",\"volume\":\"11 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-07-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Semigroup Forum\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00233-024-10459-1\",\"RegionNum\":3,\"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":"Semigroup Forum","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00233-024-10459-1","RegionNum":3,"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

1981 年，格哈德-吉尔兹（Gerhard Gierz）和吉米-劳森（Jimmie Lawson）用方程给出了一个完整网格准连续的必要条件。然而，准连续网格能否用方程来表征一直是个未知数。在本文中，我们给出了准连续完整半网格的等式特征。此外，我们还研究了类连续完全半网格的同构性。我们在 C 协同的背景下推导出准连续完全半网格的第一个同构定理。因此，我们证明了具有保留有向 sups 和非空 infs 的映射的所有连续完整半格的范畴是类连续完整半格的反射全子类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

摘要图片

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

A defining equation and reflective subcategories of quasicontinuous complete semilattices

In 1981, Gerhard Gierz and Jimmie Lawson gave a necessary condition for a complete lattice to be quasicontinuous using an equation. However, whether quasicontinuous lattices can be characterized by equations has remained unknown. In this paper, we give an equational characterization of quasicontinuous complete semilattices. Furthermore, we investigate congruences of quasicontinuous complete semilattices. We derive the first isomorphism theorem for quasicontinuous complete semilattices in the context of C-congruences. As a consequence, we show that the category of all continuous complete semilattices with maps preserving directed sups and nonempty infs is a reflective full subcategory of quasicontinuous complete semilattices.

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

Semigroup Forum 数学-数学

CiteScore

1.50

自引率

14.30%

发文量

审稿时长

12 months

期刊介绍： Semigroup Forum is a platform for speedy and efficient transmission of information on current research in semigroup theory. Scope: Algebraic semigroups, topological semigroups, partially ordered semigroups, semigroups of measures and harmonic analysis on semigroups, numerical semigroups, transformation semigroups, semigroups of operators, and applications of semigroup theory to other disciplines such as ring theory, category theory, automata, logic, etc. Languages: English (preferred), French, German, Russian. Survey Articles: Expository, such as a symposium lecture. Of any length. May include original work, but should present the nonspecialist with a reasonably elementary and self-contained account of the fundamental parts of the subject. Research Articles: Will be subject to the usual refereeing procedure. Research Announcements: Description, limited to eight pages, of new results, mostly without proofs, of full length papers appearing elsewhere. The announcement must be accompanied by a copy of the unabridged version. Short Notes: (Maximum 4 pages) Worthy of the readers'' attention, such as new proofs, significant generalizations of known facts, comments on unsolved problems, historical remarks, etc. Research Problems: Unsolved research problems. Announcements: Of conferences, seminars, and symposia on Semigroup Theory. Abstracts and Bibliographical Items: Abstracts in English, limited to one page, of completed work are solicited. Listings of books, papers, and lecture notes previously published elsewhere and, above all, of new papers for which preprints are available are solicited from all authors. Abstracts for Reviewing Journals: Authors are invited to provide with their manuscript informally a one-page abstract of their contribution with key words and phrases and with subject matter classification. This material will be forwarded to Zentralblatt für Mathematik.

期刊最新文献

Presentation of monoids generated by a projection and an involution Tropical representations of Chinese monoids with and without involution Conditionally distributive uninorms locally internal on the boundary A characterization of piecewise $$\mathscr {F}$$ -syndetic sets On the monoid of order-preserving transformations of a finite chain whose ranges are intervals