{"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}
引用次数: 0
Abstract
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.
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