{"title":"关于 n 型格序代数的一些评论和惠伊斯曼斯的一个问题","authors":"Ayşe Uyar","doi":"10.1007/s00012-024-00875-3","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, type <i>n</i> lattice-ordered algebras are introduced and a characterization is given for those of type 0 and type 1. Moreover we investigate the question: Let <i>A</i> be a lattice-ordered algebra with unit element <span>\\(e >0\\)</span> in which every positive element has an inverse. Under what conditions <i>A</i> is lattice and algebra isomorphic to <span>\\({\\mathbb {R}}\\)</span> ? We have shown that for certain algebras the question has a positive answer, generalizing thus a result of Scheffold. We also obtained a result similar to Edwards’ Theorem for normed lattice-ordered algebras.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some remarks on type n lattice-ordered algebras and a question of Huijsmans\",\"authors\":\"Ayşe Uyar\",\"doi\":\"10.1007/s00012-024-00875-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, type <i>n</i> lattice-ordered algebras are introduced and a characterization is given for those of type 0 and type 1. Moreover we investigate the question: Let <i>A</i> be a lattice-ordered algebra with unit element <span>\\\\(e >0\\\\)</span> in which every positive element has an inverse. Under what conditions <i>A</i> is lattice and algebra isomorphic to <span>\\\\({\\\\mathbb {R}}\\\\)</span> ? We have shown that for certain algebras the question has a positive answer, generalizing thus a result of Scheffold. We also obtained a result similar to Edwards’ Theorem for normed lattice-ordered algebras.</p></div>\",\"PeriodicalId\":50827,\"journal\":{\"name\":\"Algebra Universalis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-10-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra Universalis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00012-024-00875-3\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra Universalis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00012-024-00875-3","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
本文介绍了 n 型格序代数，并给出了 0 型和 1 型格序代数的特征。此外，我们还研究了一个问题：让 A 是一个具有单位元素 \(e>0\)的格有序代数，其中每个正元素都有一个逆元素。在什么条件下，A 是与 \({\mathbb {R}}\) 同构的格与代数？我们证明了对某些代数来说，这个问题有一个肯定的答案，从而推广了谢福尔德的一个结果。我们还得到了一个与规范格序代数的爱德华兹定理类似的结果。
Some remarks on type n lattice-ordered algebras and a question of Huijsmans
In this paper, type n lattice-ordered algebras are introduced and a characterization is given for those of type 0 and type 1. Moreover we investigate the question: Let A be a lattice-ordered algebra with unit element \(e >0\) in which every positive element has an inverse. Under what conditions A is lattice and algebra isomorphic to \({\mathbb {R}}\) ? We have shown that for certain algebras the question has a positive answer, generalizing thus a result of Scheffold. We also obtained a result similar to Edwards’ Theorem for normed lattice-ordered algebras.
期刊介绍：
Algebra Universalis publishes papers in universal algebra, lattice theory, and related fields. In a pragmatic way, one could define the areas of interest of the journal as the union of the areas of interest of the members of the Editorial Board. In addition to research papers, we are also interested in publishing high quality survey articles.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
