Bouligand-Severi tangents in MV-algebras

Autores
Busaniche, Manuela; Mundici, Daniele
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In their recent seminal paper published in the Annals of Pure and Applied Logic, Dubuc and Poveda call an MV-algebra A strongly semisimple if all principal quotients of A are semisimple. All boolean algebras are strongly semisimple, and so are all finitely presented MV-algebras. We show that for any 1-generator MV-algebra semisimplicity is equivalent to strong semisimplicity. Further, a semisimple 2-generator MV-algebra A is strongly semisimple if and only if its maximal spectral space m(A) does not have any rational Bouligand-Severi tangents at its rational points. In general, when A is finitely generated and m(A) has a Bouligand-Severi tangent then A is not strongly semisimple.
Fil: Busaniche, Manuela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina. Universidad Nacional del Litoral; Argentina
Fil: Mundici, Daniele. Universitá degli Studi di Firenze. Dipartimento di Matematica e Informatica; Italia
Materia
Mv-Algebra
Strongly Semisimple
Bouligand–Severi Tangent
Łukasiewicz Logic
Syntactic And Semantic Consequence
Yosida Frame
Semisimple
Logically Complete Mv-Algebra
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/13885
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Bouligand-Severi tangents in MV-algebrasBusaniche, ManuelaMundici, DanieleMv-AlgebraStrongly SemisimpleBouligand–Severi TangentŁukasiewicz LogicSyntactic And Semantic ConsequenceYosida FrameSemisimpleLogically Complete Mv-Algebrahttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In their recent seminal paper published in the Annals of Pure and Applied Logic, Dubuc and Poveda call an MV-algebra A strongly semisimple if all principal quotients of A are semisimple. All boolean algebras are strongly semisimple, and so are all finitely presented MV-algebras. We show that for any 1-generator MV-algebra semisimplicity is equivalent to strong semisimplicity. Further, a semisimple 2-generator MV-algebra A is strongly semisimple if and only if its maximal spectral space m(A) does not have any rational Bouligand-Severi tangents at its rational points. In general, when A is finitely generated and m(A) has a Bouligand-Severi tangent then A is not strongly semisimple.Fil: Busaniche, Manuela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina. Universidad Nacional del Litoral; ArgentinaFil: Mundici, Daniele. Universitá degli Studi di Firenze. Dipartimento di Matematica e Informatica; ItaliaUniversidad Autónoma de Madrid2014-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/13885Busaniche, Manuela; Mundici, Daniele; Bouligand-Severi tangents in MV-algebras; Universidad Autónoma de Madrid; Revista Matematica Iberoamericana; 30; 1; 4-2014; 191-2010213-2230enginfo:eu-repo/semantics/altIdentifier/url/http://dx.doi.org/10.4171/RMI/774info:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=30&iss=1&rank=9info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:39:12Zoai:ri.conicet.gov.ar:11336/13885instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:39:13.097CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Bouligand-Severi tangents in MV-algebras
title Bouligand-Severi tangents in MV-algebras
spellingShingle Bouligand-Severi tangents in MV-algebras
Busaniche, Manuela
Mv-Algebra
Strongly Semisimple
Bouligand–Severi Tangent
Łukasiewicz Logic
Syntactic And Semantic Consequence
Yosida Frame
Semisimple
Logically Complete Mv-Algebra
title_short Bouligand-Severi tangents in MV-algebras
title_full Bouligand-Severi tangents in MV-algebras
title_fullStr Bouligand-Severi tangents in MV-algebras
title_full_unstemmed Bouligand-Severi tangents in MV-algebras
title_sort Bouligand-Severi tangents in MV-algebras
dc.creator.none.fl_str_mv Busaniche, Manuela
Mundici, Daniele
author Busaniche, Manuela
author_facet Busaniche, Manuela
Mundici, Daniele
author_role author
author2 Mundici, Daniele
author2_role author
dc.subject.none.fl_str_mv Mv-Algebra
Strongly Semisimple
Bouligand–Severi Tangent
Łukasiewicz Logic
Syntactic And Semantic Consequence
Yosida Frame
Semisimple
Logically Complete Mv-Algebra
topic Mv-Algebra
Strongly Semisimple
Bouligand–Severi Tangent
Łukasiewicz Logic
Syntactic And Semantic Consequence
Yosida Frame
Semisimple
Logically Complete Mv-Algebra
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In their recent seminal paper published in the Annals of Pure and Applied Logic, Dubuc and Poveda call an MV-algebra A strongly semisimple if all principal quotients of A are semisimple. All boolean algebras are strongly semisimple, and so are all finitely presented MV-algebras. We show that for any 1-generator MV-algebra semisimplicity is equivalent to strong semisimplicity. Further, a semisimple 2-generator MV-algebra A is strongly semisimple if and only if its maximal spectral space m(A) does not have any rational Bouligand-Severi tangents at its rational points. In general, when A is finitely generated and m(A) has a Bouligand-Severi tangent then A is not strongly semisimple.
Fil: Busaniche, Manuela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina. Universidad Nacional del Litoral; Argentina
Fil: Mundici, Daniele. Universitá degli Studi di Firenze. Dipartimento di Matematica e Informatica; Italia
description In their recent seminal paper published in the Annals of Pure and Applied Logic, Dubuc and Poveda call an MV-algebra A strongly semisimple if all principal quotients of A are semisimple. All boolean algebras are strongly semisimple, and so are all finitely presented MV-algebras. We show that for any 1-generator MV-algebra semisimplicity is equivalent to strong semisimplicity. Further, a semisimple 2-generator MV-algebra A is strongly semisimple if and only if its maximal spectral space m(A) does not have any rational Bouligand-Severi tangents at its rational points. In general, when A is finitely generated and m(A) has a Bouligand-Severi tangent then A is not strongly semisimple.
publishDate 2014
dc.date.none.fl_str_mv 2014-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/13885
Busaniche, Manuela; Mundici, Daniele; Bouligand-Severi tangents in MV-algebras; Universidad Autónoma de Madrid; Revista Matematica Iberoamericana; 30; 1; 4-2014; 191-201
0213-2230
url http://hdl.handle.net/11336/13885
identifier_str_mv Busaniche, Manuela; Mundici, Daniele; Bouligand-Severi tangents in MV-algebras; Universidad Autónoma de Madrid; Revista Matematica Iberoamericana; 30; 1; 4-2014; 191-201
0213-2230
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://dx.doi.org/10.4171/RMI/774
info:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=30&iss=1&rank=9
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Universidad Autónoma de Madrid
publisher.none.fl_str_mv Universidad Autónoma de Madrid
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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