{"title":"Limit varieties generated by finite non-J-trivial aperiodic monoids","authors":"Olga B. Sapir","doi":"10.1007/s00233-023-10399-2","DOIUrl":null,"url":null,"abstract":"<p>Jackson and Lee proved that certain six-element monoid generates a hereditarily finitely based variety <span>\\({{\\mathbb {E}}}^1\\)</span> whose lattice of subvarieties contains an infinite ascending chain. We identify syntactic monoids which generate finitely generated subvarieties of <span>\\({{\\mathbb {E}}}^1\\)</span> and show that one of these finite monoids together with certain seven-element monoid generates a new limit variety.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00233-023-10399-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
Jackson and Lee proved that certain six-element monoid generates a hereditarily finitely based variety \({{\mathbb {E}}}^1\) whose lattice of subvarieties contains an infinite ascending chain. We identify syntactic monoids which generate finitely generated subvarieties of \({{\mathbb {E}}}^1\) and show that one of these finite monoids together with certain seven-element monoid generates a new limit variety.
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