{"title":"若干矩阵的o群上的可整除性","authors":"Ramiro H. Lafuente-Rodriguez","doi":"10.1007/s00012-022-00778-1","DOIUrl":null,"url":null,"abstract":"<div><p>We construct non-abelian totally ordered groups of matrices of finite Archimedean rank using the group of o-automorphisms of direct sums of copies of the reals ordered anti-lexicographically. We also prove that each of these o-groups is divisible, and provide, for every <span>\\(n>2\\)</span>, a specific formula to find the <i>n</i>-th root of every element of such group. Finally, we construct an example of a non-commutative totally ordered ring.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2022-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Divisibility on certain o-groups of matrices\",\"authors\":\"Ramiro H. Lafuente-Rodriguez\",\"doi\":\"10.1007/s00012-022-00778-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We construct non-abelian totally ordered groups of matrices of finite Archimedean rank using the group of o-automorphisms of direct sums of copies of the reals ordered anti-lexicographically. We also prove that each of these o-groups is divisible, and provide, for every <span>\\\\(n>2\\\\)</span>, a specific formula to find the <i>n</i>-th root of every element of such group. Finally, we construct an example of a non-commutative totally ordered ring.</p></div>\",\"PeriodicalId\":50827,\"journal\":{\"name\":\"Algebra Universalis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2022-06-25\",\"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/s00012-022-00778-1\",\"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/s00012-022-00778-1","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We construct non-abelian totally ordered groups of matrices of finite Archimedean rank using the group of o-automorphisms of direct sums of copies of the reals ordered anti-lexicographically. We also prove that each of these o-groups is divisible, and provide, for every \(n>2\), a specific formula to find the n-th root of every element of such group. Finally, we construct an example of a non-commutative totally ordered ring.
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.