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The word problem for κ-terms over the pseudovariety of local groups

2021-08-12Artigo científico Acesso aberto
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datacite.subject.fosCiências Naturais::Matemáticas
datacite.subject.sdg03:Saúde de Qualidade
datacite.subject.sdg07:Energias Renováveis e Acessíveis
datacite.subject.sdg11:Cidades e Comunidades Sustentáveis
dc.contributor.authorCosta, J. C.
dc.contributor.authorNogueira, C.
dc.contributor.authorTeixeira, M. L.
dc.date.accessioned2026-01-20T16:46:04Z
dc.date.available2026-01-20T16:46:04Z
dc.date.issued2021-08-12
dc.description.abstractIn this paper we study the κ-word problem for the pseudovariety LG of local groups, where κ is the canonical signature consisting of the multiplication and the pseudoinversion. We solve this problem by transforming each arbitrary κ-term α into another one α∗ called the LG-canonical form of α and by showing that different canonical forms have different interpretations over LG. The procedure of construction of these canonical forms consists in applying reductions determined by a set Σ of κ-identities. As a consequence, Σ is a basis of κ-identities for the κ-variety generated by LG.eng
dc.description.sponsorshipThis work was supported by the European Regional Development Fund, through the programme COMPETE, and by the Portuguese Government through FCT (Fundação para a Ciência e a Tecnologia) within the Projects UIDB/00013/2020, UIDP/00013/2020 and PEst-C/MAT/UI0013/2014.
dc.identifier.citationCosta, J.C., Nogueira, C. & Teixeira, M.L. The word problem for k-terms over the pseudovariety of local groups. Semigroup Forum 103, 439–468 (2021). https://doi.org/10.1007/s00233-021-10207-9.
dc.identifier.doi10.1007/s00233-021-10207-9
dc.identifier.eissn1432-2137
dc.identifier.issn0037-1912
dc.identifier.urihttp://hdl.handle.net/10400.8/15423
dc.language.isoeng
dc.peerreviewedyes
dc.publisherSpringer Nature
dc.relationCenter of Mathematics of the University of Minho
dc.relationCenter of Mathematics of the University of Minho
dc.relation.hasversionhttps://link.springer.com/article/10.1007/s00233-021-10207-9
dc.relation.ispartofSemigroup Forum
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectLocal group
dc.subjectPseudovariety
dc.subjectFinite semigroup
dc.subjectImplicit signature
dc.subjectWord problem
dc.subjectκ-term
dc.subjectCanonical form
dc.titleThe word problem for κ-terms over the pseudovariety of local groupseng
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleCenter of Mathematics of the University of Minho
oaire.awardTitleCenter of Mathematics of the University of Minho
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00013%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F00013%2F2020/PT
oaire.citation.endPage468
oaire.citation.startPage439
oaire.citation.titleSemigroup Forum
oaire.citation.volume103
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream6817 - DCRRNI ID
oaire.versionhttp://purl.org/coar/version/c_970fb48d4fbd8a85
person.familyNameNogueira
person.givenNameConceição
person.identifier.ciencia-id9C14-CD1D-1298
person.identifier.orcid0000-0002-9269-2221
person.identifier.scopus-author-id24339135500
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
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relation.isAuthorOfPublication.latestForDiscoveryb44ae8f7-d99a-4098-ae0b-bbf22db8f2a0
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In this paper we study the κ-word problem for the pseudovariety LG of local groups, where κ is the canonical signature consisting of the multiplication and the pseudoinversion. We solve this problem by transforming each arbitrary κ-term α into another one α∗ called the LG-canonical form of α and by showing that different canonical forms have different interpretations over LG. The procedure of construction of these canonical forms consists in applying reductions determined by a set Σ of κ-identities. As a consequence, Σ is a basis of κ-identities for the κ-variety generated by LG.
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