Algebraic properties of external numbers

Detalhes bibliográficos
Autor(a) principal: Dinis, Bruno
Data de Publicação: 2011
Outros Autores: van den Berg, Imme
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10174/3699
Resumo: Neutrices and external numbers were proposed as models of orders of magnitude within nonstandard analysis. We show that the external numbers form a commutative regular semigroup for addition and that the external numbers which are not neutrices form a commutative regular semigroup for multiplication. The validity of the distributive law is restricted, but it can be fully characterized.
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spelling Algebraic properties of external numbersneutrixexternal numberregular semigroupdistributivitynonstandard analysisNeutrices and external numbers were proposed as models of orders of magnitude within nonstandard analysis. We show that the external numbers form a commutative regular semigroup for addition and that the external numbers which are not neutrices form a commutative regular semigroup for multiplication. The validity of the distributive law is restricted, but it can be fully characterized.Journal of Logic & Analysis2012-01-17T15:37:42Z2012-01-172011-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10174/3699http://hdl.handle.net/10174/3699engJournal of Logic & Analysis 3:9 (2011) 1–301759-9008bruno.dinis@uevora.ptivdb@uevora.pt333Dinis, Brunovan den Berg, Immeinfo: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:RCAAP2024-01-03T18:41:11Zoai:dspace.uevora.pt:10174/3699Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:59:09.858650Repositório 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 Algebraic properties of external numbers
title Algebraic properties of external numbers
spellingShingle Algebraic properties of external numbers
Dinis, Bruno
neutrix
external number
regular semigroup
distributivity
nonstandard analysis
title_short Algebraic properties of external numbers
title_full Algebraic properties of external numbers
title_fullStr Algebraic properties of external numbers
title_full_unstemmed Algebraic properties of external numbers
title_sort Algebraic properties of external numbers
author Dinis, Bruno
author_facet Dinis, Bruno
van den Berg, Imme
author_role author
author2 van den Berg, Imme
author2_role author
dc.contributor.author.fl_str_mv Dinis, Bruno
van den Berg, Imme
dc.subject.por.fl_str_mv neutrix
external number
regular semigroup
distributivity
nonstandard analysis
topic neutrix
external number
regular semigroup
distributivity
nonstandard analysis
description Neutrices and external numbers were proposed as models of orders of magnitude within nonstandard analysis. We show that the external numbers form a commutative regular semigroup for addition and that the external numbers which are not neutrices form a commutative regular semigroup for multiplication. The validity of the distributive law is restricted, but it can be fully characterized.
publishDate 2011
dc.date.none.fl_str_mv 2011-01-01T00:00:00Z
2012-01-17T15:37:42Z
2012-01-17
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/10174/3699
http://hdl.handle.net/10174/3699
url http://hdl.handle.net/10174/3699
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Journal of Logic & Analysis 3:9 (2011) 1–30
1759-9008
bruno.dinis@uevora.pt
ivdb@uevora.pt
333
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Journal of Logic & Analysis
publisher.none.fl_str_mv Journal of Logic & Analysis
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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