Mobi algebra as an abstraction to the unit interval and its comparison to rings

Detalhes bibliográficos
Autor(a) principal: Fatelo, J. P.
Data de Publicação: 2019
Outros Autores: Martins-Ferreira, Nelson
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.8/3838
Resumo: This work is supported by Fundação para a Ciência e a Tecnologia (FCT) and Centro2020 through the Project references: UID/Multi/04044/2013 and PAMI – ROTEIRO/0328/2013 (No 022158) and also by CDRSP and ESTG from the Polytechnic Institute of Leiria.
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spelling Mobi algebra as an abstraction to the unit interval and its comparison to ringsgeodesic pathternary operationunit intervalunitary ringsmidpoint algebrasinvolutive medial monoidMobi algebraThis work is supported by Fundação para a Ciência e a Tecnologia (FCT) and Centro2020 through the Project references: UID/Multi/04044/2013 and PAMI – ROTEIRO/0328/2013 (No 022158) and also by CDRSP and ESTG from the Polytechnic Institute of Leiria.We introduce a new algebraic structure, called mobi algebra, consisting of three constants and one ternary operation. The canonical example of a mobi algebra is the unit interval with the three constants 0, 1, and 1/2 and the ternary operation given by the formula x−yx+yz. We study some of its properties and prove that every unitary ring with one half uniquely determines and is uniquely determined by a mobi algebra with one double. Another algebraic structure, called involutive medial monoid (IMM), is considered to establish the passage between rings and mobi algebras.Taylor & FrancisIC-OnlineFatelo, J. P.Martins-Ferreira, Nelson2019-02-19T15:07:56Z2019-01-202019-01-20T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.8/3838eng1532-4125https://doi.org/10.1080/00927872.2018.1501575info: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:RCAAP2024-01-17T15:48:01Zoai:iconline.ipleiria.pt:10400.8/3838Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:47:51.165722Repositório 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 Mobi algebra as an abstraction to the unit interval and its comparison to rings
title Mobi algebra as an abstraction to the unit interval and its comparison to rings
spellingShingle Mobi algebra as an abstraction to the unit interval and its comparison to rings
Fatelo, J. P.
geodesic path
ternary operation
unit interval
unitary rings
midpoint algebras
involutive medial monoid
Mobi algebra
title_short Mobi algebra as an abstraction to the unit interval and its comparison to rings
title_full Mobi algebra as an abstraction to the unit interval and its comparison to rings
title_fullStr Mobi algebra as an abstraction to the unit interval and its comparison to rings
title_full_unstemmed Mobi algebra as an abstraction to the unit interval and its comparison to rings
title_sort Mobi algebra as an abstraction to the unit interval and its comparison to rings
author Fatelo, J. P.
author_facet Fatelo, J. P.
Martins-Ferreira, Nelson
author_role author
author2 Martins-Ferreira, Nelson
author2_role author
dc.contributor.none.fl_str_mv IC-Online
dc.contributor.author.fl_str_mv Fatelo, J. P.
Martins-Ferreira, Nelson
dc.subject.por.fl_str_mv geodesic path
ternary operation
unit interval
unitary rings
midpoint algebras
involutive medial monoid
Mobi algebra
topic geodesic path
ternary operation
unit interval
unitary rings
midpoint algebras
involutive medial monoid
Mobi algebra
description This work is supported by Fundação para a Ciência e a Tecnologia (FCT) and Centro2020 through the Project references: UID/Multi/04044/2013 and PAMI – ROTEIRO/0328/2013 (No 022158) and also by CDRSP and ESTG from the Polytechnic Institute of Leiria.
publishDate 2019
dc.date.none.fl_str_mv 2019-02-19T15:07:56Z
2019-01-20
2019-01-20T00:00:00Z
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 http://hdl.handle.net/10400.8/3838
url http://hdl.handle.net/10400.8/3838
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1532-4125
https://doi.org/10.1080/00927872.2018.1501575
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 Taylor & Francis
publisher.none.fl_str_mv Taylor & Francis
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
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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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