{"title":"有限非j平凡非周期模群生成的极限变种","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":"{\"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}","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}
Limit varieties generated by finite non-J-trivial aperiodic monoids
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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