{"title":"On a statement of O. Frink about free pseudo-complemented meet-semilattices","authors":"Tibor Katriňák, Jaroslav Guričan","doi":"10.1007/s00012-023-00836-2","DOIUrl":null,"url":null,"abstract":"<div><p>Orrin Frink in 1962 stated incorrectly, that there exist free pseudocomplemented meet-semilattices, which are not lattices. This is disproved in the present paper. We have shown that any free PCS is in fact a sectionally pseudocomplemented lattice.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-023-00836-2.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra Universalis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00012-023-00836-2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
Orrin Frink in 1962 stated incorrectly, that there exist free pseudocomplemented meet-semilattices, which are not lattices. This is disproved in the present paper. We have shown that any free PCS is in fact a sectionally pseudocomplemented lattice.
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.
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