Baer-Levi semigroups of linear transformations
Autor(a) principal: | |
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Data de Publicação: | 2004 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://hdl.handle.net/1822/1825 |
Resumo: | Given an infinite-dimensional vector space V, we consider the semigroup GS(m,n) of all injective linear transformations of V into itself with defect n, where n is an infinite cardinal less or equal than m, the dimension of V. This is a linear version of the well-known Baer-Levi semigroup BL(p,q) defined on an infinite set X with cardinal p and where q is an infinite cardinal less or equal than p. We show that, although the basic properties of GS(m,n) are the same as those of BL(p,q), the two semigroups are never isomorphic. We also determine all left ideals of GS(m,n) and some of its maximal subsemigroups: in this, we follow previous work on BL(p,q) by Sutov (1966) and Sullivan (1978) as well as Levi and Wood (1984). |
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Baer-Levi semigroups of linear transformationsSemigroups of linear transformationsScience & TechnologyGiven an infinite-dimensional vector space V, we consider the semigroup GS(m,n) of all injective linear transformations of V into itself with defect n, where n is an infinite cardinal less or equal than m, the dimension of V. This is a linear version of the well-known Baer-Levi semigroup BL(p,q) defined on an infinite set X with cardinal p and where q is an infinite cardinal less or equal than p. We show that, although the basic properties of GS(m,n) are the same as those of BL(p,q), the two semigroups are never isomorphic. We also determine all left ideals of GS(m,n) and some of its maximal subsemigroups: in this, we follow previous work on BL(p,q) by Sutov (1966) and Sullivan (1978) as well as Levi and Wood (1984).Fundação para a Ciência e a Tecnologia (FCT) – Programa Operacional “Ciência, Tecnologia, Inovação” (POCTI).Royal Society of EdinburghUniversidade do MinhoGonçalves, Suzana MendesSullivan, R. P.20042004-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/1825eng“Proceedings section A : mathematics - The Royal Society of Edinburgh”. ISSN 0308-2105. 134:3 (2004) 477-499.0308-210510.1017/S0308210500003309info: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:RCAAP2023-10-28T01:18:15Zoai:repositorium.sdum.uminho.pt:1822/1825Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:05:00.587960Repositório 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 |
Baer-Levi semigroups of linear transformations |
title |
Baer-Levi semigroups of linear transformations |
spellingShingle |
Baer-Levi semigroups of linear transformations Gonçalves, Suzana Mendes Semigroups of linear transformations Science & Technology |
title_short |
Baer-Levi semigroups of linear transformations |
title_full |
Baer-Levi semigroups of linear transformations |
title_fullStr |
Baer-Levi semigroups of linear transformations |
title_full_unstemmed |
Baer-Levi semigroups of linear transformations |
title_sort |
Baer-Levi semigroups of linear transformations |
author |
Gonçalves, Suzana Mendes |
author_facet |
Gonçalves, Suzana Mendes Sullivan, R. P. |
author_role |
author |
author2 |
Sullivan, R. P. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Gonçalves, Suzana Mendes Sullivan, R. P. |
dc.subject.por.fl_str_mv |
Semigroups of linear transformations Science & Technology |
topic |
Semigroups of linear transformations Science & Technology |
description |
Given an infinite-dimensional vector space V, we consider the semigroup GS(m,n) of all injective linear transformations of V into itself with defect n, where n is an infinite cardinal less or equal than m, the dimension of V. This is a linear version of the well-known Baer-Levi semigroup BL(p,q) defined on an infinite set X with cardinal p and where q is an infinite cardinal less or equal than p. We show that, although the basic properties of GS(m,n) are the same as those of BL(p,q), the two semigroups are never isomorphic. We also determine all left ideals of GS(m,n) and some of its maximal subsemigroups: in this, we follow previous work on BL(p,q) by Sutov (1966) and Sullivan (1978) as well as Levi and Wood (1984). |
publishDate |
2004 |
dc.date.none.fl_str_mv |
2004 2004-01-01T00:00:00Z |
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 |
https://hdl.handle.net/1822/1825 |
url |
https://hdl.handle.net/1822/1825 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
“Proceedings section A : mathematics - The Royal Society of Edinburgh”. ISSN 0308-2105. 134:3 (2004) 477-499. 0308-2105 10.1017/S0308210500003309 |
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 |
Royal Society of Edinburgh |
publisher.none.fl_str_mv |
Royal Society of Edinburgh |
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 |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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