Topological protomodular algebras
Autor(a) principal: | |
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Data de Publicação: | 2006 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10316/4613 https://doi.org/10.1016/j.topol.2004.12.010 |
Resumo: | Topological groups have very striking properties, which have already been generalized to weaker "group like" structures, like various kinds of loops. This paper intends to show evidence that this generalization holds for a much wider class of theories, known as the protomodular theories, and which admit both an elegant categorical characterization and an easy description in universal algebra terms. Thus we propose a synthetic approach which allows to prove in a unique framework that the most striking properties of topological groups hold as well for loops or even semi-loops, rings with or without unit, associative algebras with or without unit, Lie algebras, Jordan algebras, Boolean algebras, Heyting algebras, Boolean rings, Heyting semi-lattices, and so on. |
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Topological protomodular algebrasTopological algebraAlgebraic theoryProtomodular categoryTopological groups have very striking properties, which have already been generalized to weaker "group like" structures, like various kinds of loops. This paper intends to show evidence that this generalization holds for a much wider class of theories, known as the protomodular theories, and which admit both an elegant categorical characterization and an easy description in universal algebra terms. Thus we propose a synthetic approach which allows to prove in a unique framework that the most striking properties of topological groups hold as well for loops or even semi-loops, rings with or without unit, associative algebras with or without unit, Lie algebras, Jordan algebras, Boolean algebras, Heyting algebras, Boolean rings, Heyting semi-lattices, and so on.http://www.sciencedirect.com/science/article/B6V1K-4GXVG0K-2/1/80524f4470b30ebfaf37012e4d8b45dc2006info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleaplication/PDFhttp://hdl.handle.net/10316/4613http://hdl.handle.net/10316/4613https://doi.org/10.1016/j.topol.2004.12.010engTopology and its Applications. 153:16 (2006) 3085-3100Borceux, F.Clementino, Maria Manuelinfo: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:RCAAP2020-11-06T16:59:23Zoai:estudogeral.uc.pt:10316/4613Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:00:41.598672Repositório 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 |
Topological protomodular algebras |
title |
Topological protomodular algebras |
spellingShingle |
Topological protomodular algebras Borceux, F. Topological algebra Algebraic theory Protomodular category |
title_short |
Topological protomodular algebras |
title_full |
Topological protomodular algebras |
title_fullStr |
Topological protomodular algebras |
title_full_unstemmed |
Topological protomodular algebras |
title_sort |
Topological protomodular algebras |
author |
Borceux, F. |
author_facet |
Borceux, F. Clementino, Maria Manuel |
author_role |
author |
author2 |
Clementino, Maria Manuel |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Borceux, F. Clementino, Maria Manuel |
dc.subject.por.fl_str_mv |
Topological algebra Algebraic theory Protomodular category |
topic |
Topological algebra Algebraic theory Protomodular category |
description |
Topological groups have very striking properties, which have already been generalized to weaker "group like" structures, like various kinds of loops. This paper intends to show evidence that this generalization holds for a much wider class of theories, known as the protomodular theories, and which admit both an elegant categorical characterization and an easy description in universal algebra terms. Thus we propose a synthetic approach which allows to prove in a unique framework that the most striking properties of topological groups hold as well for loops or even semi-loops, rings with or without unit, associative algebras with or without unit, Lie algebras, Jordan algebras, Boolean algebras, Heyting algebras, Boolean rings, Heyting semi-lattices, and so on. |
publishDate |
2006 |
dc.date.none.fl_str_mv |
2006 |
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 |
http://hdl.handle.net/10316/4613 http://hdl.handle.net/10316/4613 https://doi.org/10.1016/j.topol.2004.12.010 |
url |
http://hdl.handle.net/10316/4613 https://doi.org/10.1016/j.topol.2004.12.010 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Topology and its Applications. 153:16 (2006) 3085-3100 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
aplication/PDF |
dc.source.none.fl_str_mv |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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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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1799133897136537600 |