{"title":"Monounary algebras containing subalgebras with meet-irreducible congruence lattice","authors":"Lucia Janičková","doi":"10.1007/s00012-022-00786-1","DOIUrl":null,"url":null,"abstract":"<div><p>The system of all congruence lattices of all algebras with fixed base set <i>A</i> forms a lattice with respect to inclusion, denoted by <span>\\(\\mathcal {E}_A\\)</span>. Let <i>A</i> be finite. The meet-irreducible elements of <span>\\(\\mathcal {E}_A\\)</span> are congruence lattices of monounary algebras. We assume that (<i>A</i>, <i>f</i>) has a connected subalgebra <i>B</i> such that <i>B</i> contains at least 3 cyclic elements and <img> is meet-irreducible in <span>\\({\\mathcal {E}}_B\\)</span> and we prove several sufficient conditions under which <span>\\({{\\,\\mathrm{Con}\\,}}(A, f)\\)</span> is meet-irreducible in <span>\\({\\mathcal {E}}_A\\)</span>.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"83 4","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2022-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra Universalis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00012-022-00786-1","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
The system of all congruence lattices of all algebras with fixed base set A forms a lattice with respect to inclusion, denoted by \(\mathcal {E}_A\). Let A be finite. The meet-irreducible elements of \(\mathcal {E}_A\) are congruence lattices of monounary algebras. We assume that (A, f) has a connected subalgebra B such that B contains at least 3 cyclic elements and is meet-irreducible in \({\mathcal {E}}_B\) and we prove several sufficient conditions under which \({{\,\mathrm{Con}\,}}(A, f)\) is meet-irreducible in \({\mathcal {E}}_A\).
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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