{"title":"Lattice isomorphisms of orthodox semigroups with no nontrivial finite subgroups","authors":"Simon M. Goberstein","doi":"10.1007/s00233-024-10428-8","DOIUrl":null,"url":null,"abstract":"<p>Two semigroups are lattice isomorphic if their subsemigroup lattices are isomorphic, and a class of semigroups is lattice closed if it contains every semigroup which is lattice isomorphic to some semigroup from that class. An orthodox semigroup is a regular semigroup whose idempotents form a subsemigroup. We prove that the class of all orthodox semigroups having no nontrivial finite subgroups is lattice closed.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"20 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Semigroup Forum","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00233-024-10428-8","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Two semigroups are lattice isomorphic if their subsemigroup lattices are isomorphic, and a class of semigroups is lattice closed if it contains every semigroup which is lattice isomorphic to some semigroup from that class. An orthodox semigroup is a regular semigroup whose idempotents form a subsemigroup. We prove that the class of all orthodox semigroups having no nontrivial finite subgroups is lattice closed.
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