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Residual finiteness and related properties in monounary algebras and their direct products

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dc.contributor.authorDe Witt, Bill
dc.date.accessioned2021-04-27T12:30:16Z
dc.date.available2021-04-27T12:30:16Z
dc.date.issued2021-04-24
dc.identifier.citationDe Witt , B 2021 , ' Residual finiteness and related properties in monounary algebras and their direct products ' , Algebra Universalis , vol. 82 , 32 . https://doi.org/10.1007/s00012-021-00727-4en
dc.identifier.issn0002-5240
dc.identifier.otherPURE: 273673160
dc.identifier.otherPURE UUID: f5c044b8-daa9-4d81-960d-dc28d734372a
dc.identifier.otherScopus: 85104896715
dc.identifier.otherWOS: 000643253600003
dc.identifier.urihttps://hdl.handle.net/10023/23091
dc.description.abstractIn this paper we discuss the relationship between direct products of monounary algebras and their components, with respect to the properties of residual finiteness, strong/weak subalgebra separability, and complete separability. For each of these properties P, we give a criterion CP such that a monounary algebra A has property P if and only if it satisfies CP. We also show that for a direct product A×B of monounary algebras, A×B has property P if and only if one of the following is true: either both A and B have property P, or at least one of A or B are backwards-bounded, a special property which dominates direct products and which guarantees all P hold.
dc.format.extent22
dc.language.isoeng
dc.relation.ispartofAlgebra Universalisen
dc.rightsCopyright © 2021 The Author(s). Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.en
dc.subjectMonounary algebraen
dc.subjectResidually finiteen
dc.subjectDirect producten
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subjectNISen
dc.subject.lccQAen
dc.titleResidual finiteness and related properties in monounary algebras and their direct productsen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.1007/s00012-021-00727-4
dc.description.statusPeer revieweden


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