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

Detalhes bibliográficos
Autor(a) principal: Costa, J. C.
Data de Publicação: 2021
Outros Autores: Nogueira, C., Teixeira, M. L.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Texto Completo: https://hdl.handle.net/1822/87941
Resumo: 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 ∑ of κ-identities. As a consequence, ∑ is a basis of κ-identities for the κ-variety generated by LG.
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spelling The word problem for κ-terms over the pseudovariety of local groupsLocal groupPseudovarietyFinite semigroupImplicit signatureWord problemκ-termCanonical formkappa-termCiências Naturais::MatemáticasScience & TechnologyIn 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 ∑ of κ-identities. As a consequence, ∑ is a basis of κ-identities for the κ-variety generated by LG.This work was supported by the European Regional Development Fund, through the programme COMPETE, and by the Portuguese Government through FCT (Fundacao para a Ciencia e a Tecnologia) within the Projects UIDB/00013/2020, UIDP/00013/2020 and PEst-C/MAT/UI0013/2014.Springer NatureUniversidade do MinhoCosta, J. C.Nogueira, C.Teixeira, M. L.20212021-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/87941engCosta, J. C., Nogueira, C., & Teixeira, M. L. (2021, August 12). The word problem for $$\kappa $$-terms over the pseudovariety of local groups. Semigroup Forum. Springer Science and Business Media LLC. http://doi.org/10.1007/s00233-021-10207-90037-191210.1007/s00233-021-10207-9https://link.springer.com/article/10.1007/s00233-021-10207-9info:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-11-23T01:18:01Zoai:repositorium.sdum.uminho.pt:1822/87941Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T15:38:28.835030Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv The word problem for κ-terms over the pseudovariety of local groups
title The word problem for κ-terms over the pseudovariety of local groups
spellingShingle The word problem for κ-terms over the pseudovariety of local groups
Costa, J. C.
Local group
Pseudovariety
Finite semigroup
Implicit signature
Word problem
κ-term
Canonical form
kappa-term
Ciências Naturais::Matemáticas
Science & Technology
title_short The word problem for κ-terms over the pseudovariety of local groups
title_full The word problem for κ-terms over the pseudovariety of local groups
title_fullStr The word problem for κ-terms over the pseudovariety of local groups
title_full_unstemmed The word problem for κ-terms over the pseudovariety of local groups
title_sort The word problem for κ-terms over the pseudovariety of local groups
author Costa, J. C.
author_facet Costa, J. C.
Nogueira, C.
Teixeira, M. L.
author_role author
author2 Nogueira, C.
Teixeira, M. L.
author2_role author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Costa, J. C.
Nogueira, C.
Teixeira, M. L.
dc.subject.por.fl_str_mv Local group
Pseudovariety
Finite semigroup
Implicit signature
Word problem
κ-term
Canonical form
kappa-term
Ciências Naturais::Matemáticas
Science & Technology
topic Local group
Pseudovariety
Finite semigroup
Implicit signature
Word problem
κ-term
Canonical form
kappa-term
Ciências Naturais::Matemáticas
Science & Technology
description 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 ∑ of κ-identities. As a consequence, ∑ is a basis of κ-identities for the κ-variety generated by LG.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-01-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://hdl.handle.net/1822/87941
url https://hdl.handle.net/1822/87941
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Costa, J. C., Nogueira, C., & Teixeira, M. L. (2021, August 12). The word problem for $$\kappa $$-terms over the pseudovariety of local groups. Semigroup Forum. Springer Science and Business Media LLC. http://doi.org/10.1007/s00233-021-10207-9
0037-1912
10.1007/s00233-021-10207-9
https://link.springer.com/article/10.1007/s00233-021-10207-9
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer Nature
publisher.none.fl_str_mv Springer Nature
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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