The word problem for κ-terms over the pseudovariety of local groups
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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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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.European Regional Development Fund, through the programme COMPETESpringer 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/1822/87941eng0037-191210.1007/s00233-021-10207-9https://link.springer.com/article/10.1007/s00233-021-10207-9info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-01-13T01:28:11Zoai:repositorium.sdum.uminho.pt:1822/87941Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:36:12.540841Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
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 |
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:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799136837335252992 |