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Semigroup presentations for test local groups

2015-06Journal article Open access
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datacite.subject.fosCiências Naturais::Matemáticas
dc.contributor.authorCosta, J. C.
dc.contributor.authorNogueira, C.
dc.contributor.authorTeixeira, M. L.
dc.date.accessioned2025-07-15T12:09:19Z
dc.date.available2025-07-15T12:09:19Z
dc.date.issued2015-06
dc.description
dc.description.abstractIn this paper we exhibit a type of semigroup presentation which determines a class of local groups. We show that the finite elements of this class generate the pseudovariety LG of all finite local groups and use them as test-semigroups to prove that LG and S, the pseudovariety of all finite semigroups, verify the same $κ-identities involving κ-terms of rank at most 1, where κ denotes the implicit signature consisting of the multiplication and the (ω-1)-power.eng
dc.description.sponsorshipFunding text This 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, under the Project PEst-C/MAT/UI0013/2011.
dc.identifier.citationCosta, J.C., Nogueira, C. & Teixeira, M.L. Semigroup presentations for test local groups. Semigroup Forum 90, 731–752 (2015). https://doi.org/10.1007/s00233-014-9656-2
dc.identifier.doi10.1007/s00233-014-9656-2
dc.identifier.issn0037-1912
dc.identifier.issn1432-2137
dc.identifier.urihttp://hdl.handle.net/10400.8/13645
dc.language.isoeng
dc.peerreviewedyes
dc.publisherSpringer Nature
dc.relationStrategic Project - UI 13 - 2011-2012
dc.relation.hasversionhttps://link.springer.com/article/10.1007/s00233-014-9656-2
dc.relation.ispartofSemigroup Forum
dc.rights.uriN/A
dc.subjectCanonical form
dc.subjectLocal group
dc.subjectPseudovariety
dc.subjectRees matrix semigroup
dc.subjectSemigroup presentation
dc.subjectκ-term
dc.titleSemigroup presentations for test local groupseng
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleStrategic Project - UI 13 - 2011-2012
oaire.awardURIhttp://hdl.handle.net/10400.8/13643
oaire.citation.endPage752
oaire.citation.issue3
oaire.citation.startPage731
oaire.citation.titleSemigroup Forum
oaire.citation.volume90
oaire.fundingStream6820 - DCRRNI ID
oaire.versionhttp://purl.org/coar/version/c_71e4c1898caa6e32
person.familyNameNogueira
person.givenNameConceição
person.identifier.ciencia-id9C14-CD1D-1298
person.identifier.orcid0000-0002-9269-2221
person.identifier.scopus-author-id24339135500
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In this paper we exhibit a type of semigroup presentation which determines a class of local groups. We show that the finite elements of this class generate the pseudovariety LG of all finite local groups and use them as test-semigroups to prove that LG and S, the pseudovariety of all finite semigroups, verify the same $κ-identities involving κ-terms of rank at most 1, where κ denotes the implicit signature consisting of the multiplication and the (ω-1)-power.
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