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Complete reducibility of the pseudovariety LS1

2009-02Journal article Open access
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datacite.subject.fosCiências Naturais::Matemáticas
dc.contributor.authorCosta, José Carlos
dc.contributor.authorNogueira, Conceição
dc.contributor.authorNogueira, Conceição
dc.date.accessioned2025-04-15T17:41:53Z
dc.date.available2025-04-15T17:41:53Z
dc.date.issued2009-02
dc.descriptionPalavras-chave: Semigroup; pseudovariety; pseudoword; system of equations; implicit signature; complete tameness; complete reducibility; local semillatice; infinite word.
dc.description.abstractIn this paper we prove that the pseudovariety LSl of local semilattices is completely κ-reducible, where κ is the implicit signature consisting of the multiplication and the ω-power. Informally speaking, given a finite equation system with rational constraints, the existence of a solution by pseudowords of the system over LSl implies the existence of a solution by κ-words of the system over LSl satisfying the same constraints.eng
dc.description.sponsorshipBoth authors acknowledge partial support by the project PTDC/MAT/65481/2006. The work of the first author was supported, in part, by Fundação para a Ciência e a Tecnologia (FCT) through the Centro de Matemática da Universidade do Minho, which is partly funded by the European Community Fund FEDER.
dc.identifier.citationCosta, José Carlos; Nogueira, Conceição (2009). Complete Reducibility of the Pseudovariety Ls1. International Journal of Algebra and Computation. https://doi.org/10.1142/s021819670900507x.
dc.identifier.doi10.1142/s021819670900507x
dc.identifier.eissn1793-6500
dc.identifier.issn0218-1967
dc.identifier.urihttp://hdl.handle.net/10400.8/12802
dc.language.isoeng
dc.peerreviewedyes
dc.publisherWorld Scientific Pub Co Pte Ltd
dc.relationPTDC/MAT/65481/2006
dc.relation.hasversionhttps://www.worldscientific.com/doi/abs/10.1142/S021819670900507X
dc.relation.ispartofInternational Journal of Algebra and Computation
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectSemigroup
dc.subjectpseudovariety
dc.subjectpseudoword
dc.subjectsystem of equations
dc.subjectimplicit signature
dc.subjectcomplete tameness
dc.titleComplete reducibility of the pseudovariety LS1eng
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage33
oaire.citation.startPage1
oaire.citation.titleInternational Journal of Algebra and Computation
oaire.versionhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43
person.familyNameNogueira
person.givenNameConceição
person.identifier.ciencia-id9C14-CD1D-1298
person.identifier.orcid0000-0002-9269-2221
person.identifier.scopus-author-id24339135500
relation.isAuthorOfPublicationb44ae8f7-d99a-4098-ae0b-bbf22db8f2a0
relation.isAuthorOfPublication.latestForDiscoveryb44ae8f7-d99a-4098-ae0b-bbf22db8f2a0

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In this paper we prove that the pseudovariety LSl of local semilattices is completely κ-reducible, where κ is the implicit signature consisting of the multiplication and the ω-power. Informally speaking, given a finite equation system with rational constraints, the existence of a solution by pseudowords of the system over LSl implies the existence of a solution by κ-words of the system over LSl satisfying the same constraints.
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