A álgebra dos polinômios

Detalhes bibliográficos
Autor(a) principal: Sousa, Reginaldo Jacinto de
Data de Publicação: 2020
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da UFG
Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/10779
Resumo: In this work, we will approach the definition of polynomial using the concept of sequence, which allows you to remove the ambiguity from the symbol x, and we will study the algebraic structure of the polynomial rings, the concept and criteria of polynomial irreducibility and factoring of a polynomial in the product of irreducible polynomials, aiming to provide mathematics teachers who work in high school, a deepening in the study of abstract algebra. Obtaining, some suggestions of applications in the classroom, for example, the study of the rationality of a given number.
id UFG-2_24323740c19f51eb58acba3b3819aba5
oai_identifier_str oai:repositorio.bc.ufg.br:tede/10779
network_acronym_str UFG-2
network_name_str Repositório Institucional da UFG
repository_id_str
spelling Dias , Ivonildes Ribeiro Martinshttp://lattes.cnpq.br/8664599889120339Dias , Ivonildes Ribeiro MartinsMartins, Ivonildes RibeiroAssis, Aline Mota de Mesquitahttp://lattes.cnpq.br/0141261662522620Sousa, Reginaldo Jacinto de2020-09-22T16:03:20Z2020-09-22T16:03:20Z2020-05-28SOUSA, R. J. A álgebra dos polinômios. 2020. 84 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2020.http://repositorio.bc.ufg.br/tede/handle/tede/10779In this work, we will approach the definition of polynomial using the concept of sequence, which allows you to remove the ambiguity from the symbol x, and we will study the algebraic structure of the polynomial rings, the concept and criteria of polynomial irreducibility and factoring of a polynomial in the product of irreducible polynomials, aiming to provide mathematics teachers who work in high school, a deepening in the study of abstract algebra. Obtaining, some suggestions of applications in the classroom, for example, the study of the rationality of a given number.Neste trabalho, abordaremos a definição de polinômio utilizando o conceito de sequência, a qual permite remover a ambiguidade do símbolo x, e estudaremos a estrutura algébrica dos anéis de polinômios, o conceito e os critérios de irredutibilidade polinomial e fatoração de um polinômio em produto de polinômios irredutíveis, tendo como objetivo fornecer aos professores de Matemática que atuam no Ensino Médio, um aprofundamento no estudo da álgebra abstrata. Obtendo, algumas sugestões de aplicações em sala de aula, por exemplo, o estudo da racionalidade de um determinado número.Submitted by Franciele Moreira (francielemoreyra@gmail.com) on 2020-09-22T15:10:15Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Dissertação - Reginaldo Jacinto de Sousa - 2020.pdf: 1304530 bytes, checksum: 31bbd5415a445dbd6d57a9ae2476325a (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2020-09-22T16:03:19Z (GMT) No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Dissertação - Reginaldo Jacinto de Sousa - 2020.pdf: 1304530 bytes, checksum: 31bbd5415a445dbd6d57a9ae2476325a (MD5)Made available in DSpace on 2020-09-22T16:03:20Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Dissertação - Reginaldo Jacinto de Sousa - 2020.pdf: 1304530 bytes, checksum: 31bbd5415a445dbd6d57a9ae2476325a (MD5) Previous issue date: 2020-05-28porUniversidade Federal de GoiásPROFMAT - Programa de Pós-graduação em Matemática em Rede Nacional - Sociedade Brasileira de Matemática (IME)UFGBrasilInstituto de Matemática e Estatística - IME (RG)Attribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessÁlgebraAnéis de polinômiosIrredutibilidade polinomialAlgebraPolynomial ringsIrreducibility polynomialCIENCIAS EXATAS E DA TERRA::MATEMATICAA álgebra dos polinômiosThe algebra of polynomiesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis6750050050027187reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGLICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://repositorio.bc.ufg.br/tede/bitstreams/f3a5d03e-f4a9-4a15-bd1b-9a13e70f75c9/download8a4605be74aa9ea9d79846c1fba20a33MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811http://repositorio.bc.ufg.br/tede/bitstreams/208678e8-16d8-4289-ad38-ba1bbb331295/downloade39d27027a6cc9cb039ad269a5db8e34MD52ORIGINALDissertação - Reginaldo Jacinto de Sousa - 2020.pdfDissertação - Reginaldo Jacinto de Sousa - 2020.pdfapplication/pdf1304530http://repositorio.bc.ufg.br/tede/bitstreams/b09cfb51-0616-4ebf-b099-7823b7139b76/download31bbd5415a445dbd6d57a9ae2476325aMD53tede/107792020-09-22 13:03:20.563http://creativecommons.org/licenses/by-nc-nd/3.0/br/Attribution-NonCommercial-NoDerivs 3.0 Brazilopen.accessoai:repositorio.bc.ufg.br:tede/10779http://repositorio.bc.ufg.br/tedeRepositório InstitucionalPUBhttp://repositorio.bc.ufg.br/oai/requesttasesdissertacoes.bc@ufg.bropendoar:2020-09-22T16:03:20Repositório Institucional da UFG - Universidade Federal de Goiás (UFG)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
dc.title.pt_BR.fl_str_mv A álgebra dos polinômios
dc.title.alternative.eng.fl_str_mv The algebra of polynomies
title A álgebra dos polinômios
spellingShingle A álgebra dos polinômios
Sousa, Reginaldo Jacinto de
Álgebra
Anéis de polinômios
Irredutibilidade polinomial
Algebra
Polynomial rings
Irreducibility polynomial
CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short A álgebra dos polinômios
title_full A álgebra dos polinômios
title_fullStr A álgebra dos polinômios
title_full_unstemmed A álgebra dos polinômios
title_sort A álgebra dos polinômios
author Sousa, Reginaldo Jacinto de
author_facet Sousa, Reginaldo Jacinto de
author_role author
dc.contributor.advisor1.fl_str_mv Dias , Ivonildes Ribeiro Martins
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/8664599889120339
dc.contributor.referee1.fl_str_mv Dias , Ivonildes Ribeiro Martins
dc.contributor.referee2.fl_str_mv Martins, Ivonildes Ribeiro
dc.contributor.referee3.fl_str_mv Assis, Aline Mota de Mesquita
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/0141261662522620
dc.contributor.author.fl_str_mv Sousa, Reginaldo Jacinto de
contributor_str_mv Dias , Ivonildes Ribeiro Martins
Dias , Ivonildes Ribeiro Martins
Martins, Ivonildes Ribeiro
Assis, Aline Mota de Mesquita
dc.subject.por.fl_str_mv Álgebra
Anéis de polinômios
Irredutibilidade polinomial
topic Álgebra
Anéis de polinômios
Irredutibilidade polinomial
Algebra
Polynomial rings
Irreducibility polynomial
CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.eng.fl_str_mv Algebra
Polynomial rings
Irreducibility polynomial
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA
description In this work, we will approach the definition of polynomial using the concept of sequence, which allows you to remove the ambiguity from the symbol x, and we will study the algebraic structure of the polynomial rings, the concept and criteria of polynomial irreducibility and factoring of a polynomial in the product of irreducible polynomials, aiming to provide mathematics teachers who work in high school, a deepening in the study of abstract algebra. Obtaining, some suggestions of applications in the classroom, for example, the study of the rationality of a given number.
publishDate 2020
dc.date.accessioned.fl_str_mv 2020-09-22T16:03:20Z
dc.date.available.fl_str_mv 2020-09-22T16:03:20Z
dc.date.issued.fl_str_mv 2020-05-28
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 SOUSA, R. J. A álgebra dos polinômios. 2020. 84 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2020.
dc.identifier.uri.fl_str_mv http://repositorio.bc.ufg.br/tede/handle/tede/10779
identifier_str_mv SOUSA, R. J. A álgebra dos polinômios. 2020. 84 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2020.
url http://repositorio.bc.ufg.br/tede/handle/tede/10779
dc.language.iso.fl_str_mv por
language por
dc.relation.program.fl_str_mv 67
dc.relation.confidence.fl_str_mv 500
500
500
dc.relation.department.fl_str_mv 27
dc.relation.cnpq.fl_str_mv 187
dc.rights.driver.fl_str_mv Attribution-NonCommercial-NoDerivs 3.0 Brazil
http://creativecommons.org/licenses/by-nc-nd/3.0/br/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivs 3.0 Brazil
http://creativecommons.org/licenses/by-nc-nd/3.0/br/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Universidade Federal de Goiás
dc.publisher.program.fl_str_mv PROFMAT - Programa de Pós-graduação em Matemática em Rede Nacional - Sociedade Brasileira de Matemática (IME)
dc.publisher.initials.fl_str_mv UFG
dc.publisher.country.fl_str_mv Brasil
dc.publisher.department.fl_str_mv Instituto de Matemática e Estatística - IME (RG)
publisher.none.fl_str_mv Universidade Federal de Goiás
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFG
instname:Universidade Federal de Goiás (UFG)
instacron:UFG
instname_str Universidade Federal de Goiás (UFG)
instacron_str UFG
institution UFG
reponame_str Repositório Institucional da UFG
collection Repositório Institucional da UFG
bitstream.url.fl_str_mv http://repositorio.bc.ufg.br/tede/bitstreams/f3a5d03e-f4a9-4a15-bd1b-9a13e70f75c9/download
http://repositorio.bc.ufg.br/tede/bitstreams/208678e8-16d8-4289-ad38-ba1bbb331295/download
http://repositorio.bc.ufg.br/tede/bitstreams/b09cfb51-0616-4ebf-b099-7823b7139b76/download
bitstream.checksum.fl_str_mv 8a4605be74aa9ea9d79846c1fba20a33
e39d27027a6cc9cb039ad269a5db8e34
31bbd5415a445dbd6d57a9ae2476325a
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
repository.name.fl_str_mv Repositório Institucional da UFG - Universidade Federal de Goiás (UFG)
repository.mail.fl_str_mv tasesdissertacoes.bc@ufg.br
_version_ 1798044337719738368

Registros relacionados