Sistemas de reescrita para grupos policíclicos
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFG |
Texto Completo: | http://repositorio.bc.ufg.br/tede/handle/tede/4552 |
Resumo: | In this work we consider monoid presentations MonhX,Ri, with set of generators X and relations R, defining groups and monoids as equivalence classes of words over X, in relation to a congruence generated by R. Taking R as a rewriting system with respect to an linear ordering of X , the set of words over X, we can apply some rewriting strategies in its laws. We use a version of the Knuth-Bendix method in R to find a confluent rewriting system equivalent to original, when such finite system exist. This new set of relations, denoted by RC(X, R), allows that in MonhX,Ri any element be defined by a unique irreducible word with respect to RC(X, R). We exhibit several examples of the execution of the Knuth-Bendix method from the functions of KBMAG package of the GAP system. Lastly, we set up a sufficient condition so that certain monoid presentations for polycyclic groups be confluent. |
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Oliveira, Ricardo Nunes dehttp://lattes.cnpq.br/0563210461148997Rodrigues, Paulo Henrique de AzevedoOliveira, Ricardo Nunes deDias, Ivonildes Ribeiro MartinsBerlatto, Adilson Antôniohttp://lattes.cnpq.br/4385129955964826Santos, Laredo Rennan Pereira2015-05-19T15:54:12Z2015-02-25SANTOS, L. R. P. Sistemas de reescrita para grupos policíclicos. 2015. 136 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2015.http://repositorio.bc.ufg.br/tede/handle/tede/4552ark:/38995/001300000f83rIn this work we consider monoid presentations MonhX,Ri, with set of generators X and relations R, defining groups and monoids as equivalence classes of words over X, in relation to a congruence generated by R. Taking R as a rewriting system with respect to an linear ordering of X , the set of words over X, we can apply some rewriting strategies in its laws. We use a version of the Knuth-Bendix method in R to find a confluent rewriting system equivalent to original, when such finite system exist. This new set of relations, denoted by RC(X, R), allows that in MonhX,Ri any element be defined by a unique irreducible word with respect to RC(X, R). We exhibit several examples of the execution of the Knuth-Bendix method from the functions of KBMAG package of the GAP system. Lastly, we set up a sufficient condition so that certain monoid presentations for polycyclic groups be confluent.Neste trabalho, consideramos apresentações monoidais MonhX,Ri, com conjunto de geradores X e de relações R, definindo grupos e monoides como classes de equivalência de palavras sobre X, em relação a uma congruência gerada por R. Tomando R como um sistema de reescrita com respeito à uma ordenação linear de X , o conjunto de palavras sobre X, podemos aplicar algumas estratégias de reescrita em suas leis. Usamos uma versão do método de Knuth-Bendix em R para encontrar um sistema de reescrita confluente que seja equivalente ao original, quando um tal sistema finito existe. Este novo conjunto de relações, denotado por RC(X, R), permite que em MonhX,Ri qualquer elemento seja definido por uma única palavra irredutível com respeito a RC(X, R). Exibimos diversos exemplos da execução do método de Knuth-Bendix a partir das funções do pacote KBMAG do sistema GAP. Por fim, estabelecemos uma condição suficiente para que certas apresentações monoidais para grupos policíclicos sejam confluentes.Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-05-19T15:51:20Z No. of bitstreams: 2 Dissertação - Laredo Rennan Pereira Santos - 2015.pdf: 970933 bytes, checksum: 6b8836c42db993ababe18805a5857373 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-05-19T15:54:12Z (GMT) No. of bitstreams: 2 Dissertação - Laredo Rennan Pereira Santos - 2015.pdf: 970933 bytes, checksum: 6b8836c42db993ababe18805a5857373 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Made available in DSpace on 2015-05-19T15:54:12Z (GMT). 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dc.title.por.fl_str_mv |
Sistemas de reescrita para grupos policíclicos |
dc.title.alternative.eng.fl_str_mv |
Rewriting systems for polycyclic groups |
title |
Sistemas de reescrita para grupos policíclicos |
spellingShingle |
Sistemas de reescrita para grupos policíclicos Santos, Laredo Rennan Pereira Monoides Sistemas de reescrita Knuth-bendix KBMAG Grupos policíclicos Monoids Rewriting systems Knuth-bendix KBMAG Polycyclic groups CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Sistemas de reescrita para grupos policíclicos |
title_full |
Sistemas de reescrita para grupos policíclicos |
title_fullStr |
Sistemas de reescrita para grupos policíclicos |
title_full_unstemmed |
Sistemas de reescrita para grupos policíclicos |
title_sort |
Sistemas de reescrita para grupos policíclicos |
author |
Santos, Laredo Rennan Pereira |
author_facet |
Santos, Laredo Rennan Pereira |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Oliveira, Ricardo Nunes de |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/0563210461148997 |
dc.contributor.referee1.fl_str_mv |
Rodrigues, Paulo Henrique de Azevedo |
dc.contributor.referee2.fl_str_mv |
Oliveira, Ricardo Nunes de |
dc.contributor.referee3.fl_str_mv |
Dias, Ivonildes Ribeiro Martins |
dc.contributor.referee4.fl_str_mv |
Berlatto, Adilson Antônio |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/4385129955964826 |
dc.contributor.author.fl_str_mv |
Santos, Laredo Rennan Pereira |
contributor_str_mv |
Oliveira, Ricardo Nunes de Rodrigues, Paulo Henrique de Azevedo Oliveira, Ricardo Nunes de Dias, Ivonildes Ribeiro Martins Berlatto, Adilson Antônio |
dc.subject.por.fl_str_mv |
Monoides Sistemas de reescrita Knuth-bendix KBMAG Grupos policíclicos |
topic |
Monoides Sistemas de reescrita Knuth-bendix KBMAG Grupos policíclicos Monoids Rewriting systems Knuth-bendix KBMAG Polycyclic groups CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Monoids Rewriting systems Knuth-bendix KBMAG Polycyclic groups |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
In this work we consider monoid presentations MonhX,Ri, with set of generators X and relations R, defining groups and monoids as equivalence classes of words over X, in relation to a congruence generated by R. Taking R as a rewriting system with respect to an linear ordering of X , the set of words over X, we can apply some rewriting strategies in its laws. We use a version of the Knuth-Bendix method in R to find a confluent rewriting system equivalent to original, when such finite system exist. This new set of relations, denoted by RC(X, R), allows that in MonhX,Ri any element be defined by a unique irreducible word with respect to RC(X, R). We exhibit several examples of the execution of the Knuth-Bendix method from the functions of KBMAG package of the GAP system. Lastly, we set up a sufficient condition so that certain monoid presentations for polycyclic groups be confluent. |
publishDate |
2015 |
dc.date.accessioned.fl_str_mv |
2015-05-19T15:54:12Z |
dc.date.issued.fl_str_mv |
2015-02-25 |
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 |
SANTOS, L. R. P. Sistemas de reescrita para grupos policíclicos. 2015. 136 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2015. |
dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tede/4552 |
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ark:/38995/001300000f83r |
identifier_str_mv |
SANTOS, L. R. P. Sistemas de reescrita para grupos policíclicos. 2015. 136 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2015. ark:/38995/001300000f83r |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/4552 |
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por |
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por |
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6600717948137941247 |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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openAccess |
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Universidade Federal de Goiás |
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UFG |
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Brasil |
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Instituto de Matemática e Estatística - IME (RG) |
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Universidade Federal de Goiás |
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