Ideais Completos

Detalhes bibliográficos
Ano de defesa: 2023
Autor(a) principal: RIBEIRO, Ranney Ritchie Souto lattes
Orientador(a): LIMA, Pedro Henrique Apoliano Albuquerque lattes
Banca de defesa: LIMA, Pedro Henrique A. A. lattes, MARÃO, José Antônio Pires Ferreira lattes, PÉREZ, Victor Hugo Jorge lattes
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Universidade Federal do Maranhão
Programa de Pós-Graduação: PROGRAMA DE PÓS-GRADUAÇÃO EM MATEMÁTICA/CCET
Departamento: COORDENAÇÃO DO CURSO DE CIÊNCIA E TECNOLOGIA/CCET
País: Brasil
Palavras-chave em Português:
ideal basicamente completo;
ideal contraído;
ideal completo;
ideal m-completo;
propriedade de Rees;
ideal integralmente fechado
Palavras-chave em Inglês:
Basically full ideal;
contracted ideal;
full ideal;
m-full ideal;
Rees property;
integrally closed ideal
Área do conhecimento CNPq:
Geometria Algebrica
Link de acesso: https://tedebc.ufma.br/jspui/handle/tede/5479
Resumo: The theory of integrally closed ideals in two-dimensional regular local rings (R,m) was introduced by the mathematician Oscar Ascher Zariski. Zariski’s motivation was to give algebraic meaning to the idea of complete linear systems of curves. He studied the class of the contracted ideals. It is known that contracted m-primary ideals I of R are characterized by the following property: (I : m) = (I : x) for some x ∈ m\m2. We call the ideals with this property full ideals and compare this class of ideals with the classes of m-full ideals, basically full ideals and contracted ideals in regular local rings of dimension greater than 2. The m-full ideals are easily seen as full. In this dissertation, we find a sufficient condition for a full ideal to be m-full. We also show that full, m-full, contracted, integrally closed and normal ideals are all equivalents in case of an ideal of parameter. We find a sufficient condition for a basically full parameter ideal to be full.
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spelling LIMA, Pedro Henrique Apoliano Albuquerquehttp://lattes.cnpq.br/1598281978467904LIMA, Pedro Henrique A. A.http://lattes.cnpq.br/1598281978467904MARÃO, José Antônio Pires Ferreirahttp://lattes.cnpq.br/4501761863997440PÉREZ, Victor Hugo Jorgehttp://lattes.cnpq.br/7108890546757762http://lattes.cnpq.br/2705882775830141RIBEIRO, Ranney Ritchie Souto2024-08-29T14:03:43Z2023-05-12RIBEIRO, Ranney Ritchie Souto. Ideais Completos. 2023. 62 f. Dissertação( Programa de Pós-graduação em Matemática/CCET) - Universidade Federal do Maranhão, São Luís, 2023.https://tedebc.ufma.br/jspui/handle/tede/5479The theory of integrally closed ideals in two-dimensional regular local rings (R,m) was introduced by the mathematician Oscar Ascher Zariski. Zariski’s motivation was to give algebraic meaning to the idea of complete linear systems of curves. He studied the class of the contracted ideals. It is known that contracted m-primary ideals I of R are characterized by the following property: (I : m) = (I : x) for some x ∈ m\m2. We call the ideals with this property full ideals and compare this class of ideals with the classes of m-full ideals, basically full ideals and contracted ideals in regular local rings of dimension greater than 2. The m-full ideals are easily seen as full. In this dissertation, we find a sufficient condition for a full ideal to be m-full. We also show that full, m-full, contracted, integrally closed and normal ideals are all equivalents in case of an ideal of parameter. We find a sufficient condition for a basically full parameter ideal to be full.A teoria de ideais integralmente fechados em anéis locais regulares bidimensionais (R,m) foi introduzida pelo matemático Oscar Ascher Zariski. A motivação de Zariski foi dar um significado algébrico para a ideia de sistemas lineares completos de curvas. Ele estudou a classe dos ideais contraídos. Sabe-se que os ideais m-primários contraídos I de R são caracterizados pela seguinte propriedade: (I : m) = (I : x) para algum x ∈ m\m2. Chamamos os ideais com essa propriedade de ideais completos e comparamos essa classe com as classes dos ideais m-completos, basicamente completos e contraídos em anéis locais regulares de dimensão superior a dois. Os ideais m-completos são facilmente vistos como completos. Neste trabalho, encontramos uma condição suficiente para que um ideal completo seja m-completo. Mostramos também que ideais completos, m-completos, contraídos, integralmente fechados e normais são todos equivalentes no caso em que o ideal é de parâmetro. Encontramos uma condição suficiente para que um ideal de parâmetro basicamente completo seja completo.Submitted by Maria Aparecida (cidazen@gmail.com) on 2024-08-29T14:03:43Z No. of bitstreams: 1 RANNEY_RITCHIE.pdf: 919954 bytes, checksum: 9a94a641028e9018bf5afa387608f3cf (MD5)Made available in DSpace on 2024-08-29T14:03:43Z (GMT). No. of bitstreams: 1 RANNEY_RITCHIE.pdf: 919954 bytes, checksum: 9a94a641028e9018bf5afa387608f3cf (MD5) Previous issue date: 2023-05-12FAPEMAapplication/pdfporUniversidade Federal do MaranhãoPROGRAMA DE PÓS-GRADUAÇÃO EM MATEMÁTICA/CCETUFMABrasilCOORDENAÇÃO DO CURSO DE CIÊNCIA E TECNOLOGIA/CCETideal basicamente completo;ideal contraído;ideal completo;ideal m-completo;propriedade de Rees;ideal integralmente fechadoBasically full ideal;contracted ideal;full ideal;m-full ideal;Rees property;integrally closed idealGeometria AlgebricaIdeais CompletosComplete Idealsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccessreponame:Biblioteca Digital de Teses e Dissertações da UFMAinstname:Universidade Federal do Maranhão (UFMA)instacron:UFMAORIGINALRANNEY_RITCHIE.pdfRANNEY_RITCHIE.pdfapplication/pdf919954http://tedebc.ufma.br:8080/bitstream/tede/5479/2/RANNEY_RITCHIE.pdf9a94a641028e9018bf5afa387608f3cfMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-82255http://tedebc.ufma.br:8080/bitstream/tede/5479/1/license.txt97eeade1fce43278e63fe063657f8083MD51tede/54792024-08-29 11:03:43.482oai:tede2: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Biblioteca Digital de Teses e Dissertaçõeshttps://tedebc.ufma.br/jspui/PUBhttp://tedebc.ufma.br:8080/oai/requestrepositorio@ufma.br||repositorio@ufma.bropendoar:21312024-08-29T14:03:43Biblioteca Digital de Teses e Dissertações da UFMA - Universidade Federal do Maranhão (UFMA)false
dc.title.por.fl_str_mv Ideais Completos
dc.title.alternative.eng.fl_str_mv Complete Ideals
title Ideais Completos
spellingShingle Ideais Completos
RIBEIRO, Ranney Ritchie Souto
ideal basicamente completo;
ideal contraído;
ideal completo;
ideal m-completo;
propriedade de Rees;
ideal integralmente fechado
Basically full ideal;
contracted ideal;
full ideal;
m-full ideal;
Rees property;
integrally closed ideal
Geometria Algebrica
title_short Ideais Completos
title_full Ideais Completos
title_fullStr Ideais Completos
title_full_unstemmed Ideais Completos
title_sort Ideais Completos
author RIBEIRO, Ranney Ritchie Souto
author_facet RIBEIRO, Ranney Ritchie Souto
author_role author
dc.contributor.advisor1.fl_str_mv LIMA, Pedro Henrique Apoliano Albuquerque
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/1598281978467904
dc.contributor.referee1.fl_str_mv LIMA, Pedro Henrique A. A.
dc.contributor.referee1Lattes.fl_str_mv http://lattes.cnpq.br/1598281978467904
dc.contributor.referee2.fl_str_mv MARÃO, José Antônio Pires Ferreira
dc.contributor.referee2Lattes.fl_str_mv http://lattes.cnpq.br/4501761863997440
dc.contributor.referee3.fl_str_mv PÉREZ, Victor Hugo Jorge
dc.contributor.referee3Lattes.fl_str_mv http://lattes.cnpq.br/7108890546757762
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/2705882775830141
dc.contributor.author.fl_str_mv RIBEIRO, Ranney Ritchie Souto
contributor_str_mv LIMA, Pedro Henrique Apoliano Albuquerque
LIMA, Pedro Henrique A. A.
MARÃO, José Antônio Pires Ferreira
PÉREZ, Victor Hugo Jorge
dc.subject.por.fl_str_mv ideal basicamente completo;
ideal contraído;
ideal completo;
ideal m-completo;
propriedade de Rees;
ideal integralmente fechado
topic ideal basicamente completo;
ideal contraído;
ideal completo;
ideal m-completo;
propriedade de Rees;
ideal integralmente fechado
Basically full ideal;
contracted ideal;
full ideal;
m-full ideal;
Rees property;
integrally closed ideal
Geometria Algebrica
dc.subject.eng.fl_str_mv Basically full ideal;
contracted ideal;
full ideal;
m-full ideal;
Rees property;
integrally closed ideal
dc.subject.cnpq.fl_str_mv Geometria Algebrica
description The theory of integrally closed ideals in two-dimensional regular local rings (R,m) was introduced by the mathematician Oscar Ascher Zariski. Zariski’s motivation was to give algebraic meaning to the idea of complete linear systems of curves. He studied the class of the contracted ideals. It is known that contracted m-primary ideals I of R are characterized by the following property: (I : m) = (I : x) for some x ∈ m\m2. We call the ideals with this property full ideals and compare this class of ideals with the classes of m-full ideals, basically full ideals and contracted ideals in regular local rings of dimension greater than 2. The m-full ideals are easily seen as full. In this dissertation, we find a sufficient condition for a full ideal to be m-full. We also show that full, m-full, contracted, integrally closed and normal ideals are all equivalents in case of an ideal of parameter. We find a sufficient condition for a basically full parameter ideal to be full.
publishDate 2023
dc.date.issued.fl_str_mv 2023-05-12
dc.date.accessioned.fl_str_mv 2024-08-29T14:03:43Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.citation.fl_str_mv RIBEIRO, Ranney Ritchie Souto. Ideais Completos. 2023. 62 f. Dissertação( Programa de Pós-graduação em Matemática/CCET) - Universidade Federal do Maranhão, São Luís, 2023.
dc.identifier.uri.fl_str_mv https://tedebc.ufma.br/jspui/handle/tede/5479
identifier_str_mv RIBEIRO, Ranney Ritchie Souto. Ideais Completos. 2023. 62 f. Dissertação( Programa de Pós-graduação em Matemática/CCET) - Universidade Federal do Maranhão, São Luís, 2023.
url https://tedebc.ufma.br/jspui/handle/tede/5479
dc.language.iso.fl_str_mv por
language por
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 Universidade Federal do Maranhão
dc.publisher.program.fl_str_mv PROGRAMA DE PÓS-GRADUAÇÃO EM MATEMÁTICA/CCET
dc.publisher.initials.fl_str_mv UFMA
dc.publisher.country.fl_str_mv Brasil
dc.publisher.department.fl_str_mv COORDENAÇÃO DO CURSO DE CIÊNCIA E TECNOLOGIA/CCET
publisher.none.fl_str_mv Universidade Federal do Maranhão
dc.source.none.fl_str_mv reponame:Biblioteca Digital de Teses e Dissertações da UFMA
instname:Universidade Federal do Maranhão (UFMA)
instacron:UFMA
instname_str Universidade Federal do Maranhão (UFMA)
instacron_str UFMA
institution UFMA
reponame_str Biblioteca Digital de Teses e Dissertações da UFMA
collection Biblioteca Digital de Teses e Dissertações da UFMA
bitstream.url.fl_str_mv http://tedebc.ufma.br:8080/bitstream/tede/5479/2/RANNEY_RITCHIE.pdf
http://tedebc.ufma.br:8080/bitstream/tede/5479/1/license.txt
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