{"title":"关于泛代数几何的个数","authors":"Erhard Aichinger, Bernardo Rossi","doi":"10.1007/s00012-022-00797-y","DOIUrl":null,"url":null,"abstract":"<div><p>The <i>algebraic geometry</i> of a universal algebra <span>\\({\\textbf{A}}\\)</span> is defined as the collection of solution sets of systems of term equations. Two algebras <span>\\({\\textbf{A}}_1\\)</span> and <span>\\({\\textbf{A}}_2\\)</span> are called <i>algebraically equivalent</i> if they have the same algebraic geometry. We prove that on a finite set <i>A</i> with <span>\\(|A|\\)</span> there are countably many algebraically inequivalent Mal’cev algebras and that on a finite set <i>A</i> with <span>\\(|A|\\)</span> there are continuously many algebraically inequivalent algebras.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-022-00797-y.pdf","citationCount":"1","resultStr":"{\"title\":\"On the number of universal algebraic geometries\",\"authors\":\"Erhard Aichinger, Bernardo Rossi\",\"doi\":\"10.1007/s00012-022-00797-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The <i>algebraic geometry</i> of a universal algebra <span>\\\\({\\\\textbf{A}}\\\\)</span> is defined as the collection of solution sets of systems of term equations. Two algebras <span>\\\\({\\\\textbf{A}}_1\\\\)</span> and <span>\\\\({\\\\textbf{A}}_2\\\\)</span> are called <i>algebraically equivalent</i> if they have the same algebraic geometry. We prove that on a finite set <i>A</i> with <span>\\\\(|A|\\\\)</span> there are countably many algebraically inequivalent Mal’cev algebras and that on a finite set <i>A</i> with <span>\\\\(|A|\\\\)</span> there are continuously many algebraically inequivalent algebras.</p></div>\",\"PeriodicalId\":50827,\"journal\":{\"name\":\"Algebra Universalis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2022-11-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00012-022-00797-y.pdf\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra Universalis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00012-022-00797-y\",\"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/s00012-022-00797-y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
The algebraic geometry of a universal algebra \({\textbf{A}}\) is defined as the collection of solution sets of systems of term equations. Two algebras \({\textbf{A}}_1\) and \({\textbf{A}}_2\) are called algebraically equivalent if they have the same algebraic geometry. We prove that on a finite set A with \(|A|\) there are countably many algebraically inequivalent Mal’cev algebras and that on a finite set A with \(|A|\) there are continuously many algebraically inequivalent 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
