Injective linear transformations with equal gap and defect

Detalhes bibliográficos
Autor(a) principal: Araújo, C. Mendes
Data de Publicação: 2022
Outros Autores: Gonçalves, Suzana Mendes
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://hdl.handle.net/1822/79996
Resumo: Suppose V is an infinite-dimensional vector space over a field F and let I(V) denote the inverse semigroup of all injective partial linear transformations on V. Given ß in I(V), we denote the domain and the range of ß by dom ß and im ß, respectively, and we call the cardinals g(ß)=codim(domß) and d(ß)=codim(imß) the `gap' and the `defect' of ß, respectively. In this paper, we study the semigroup A(V) of all injective partial linear transformations with equal gap and defect, and characterise Green's relations and ideals in A(V). This is analogous to work by Sanwong and Sullivan in 2009 on a similarly-defined semigroup for the set case, but we show that these semigroups are never isomorphic.
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spelling Injective linear transformations with equal gap and defectidealsGreen's relationsInjective linear transformationsQuasiresidualsCiências Naturais::MatemáticasScience & TechnologySuppose V is an infinite-dimensional vector space over a field F and let I(V) denote the inverse semigroup of all injective partial linear transformations on V. Given ß in I(V), we denote the domain and the range of ß by dom ß and im ß, respectively, and we call the cardinals g(ß)=codim(domß) and d(ß)=codim(imß) the `gap' and the `defect' of ß, respectively. In this paper, we study the semigroup A(V) of all injective partial linear transformations with equal gap and defect, and characterise Green's relations and ideals in A(V). This is analogous to work by Sanwong and Sullivan in 2009 on a similarly-defined semigroup for the set case, but we show that these semigroups are never isomorphic.The research of the authors was partially financed by Portuguese Funds through FCT (Fundação para a Ciência e a Tecnologia) within the Projects UIDB/00013/2020 and UIDP/00013/2020.Cambridge University PressUniversidade do MinhoAraújo, C. MendesGonçalves, Suzana Mendes2022-022022-02-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/79996engMendes Araújo, C., & Mendes-Gonçalves, S. (2022). Injective linear transformations with equal gap and defect. Bulletin of the Australian Mathematical Society, 105(1), 106-116. doi:10.1017/S00049727210003440004-97271755-163310.1017/S0004972721000344https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/abs/injective-linear-transformations-with-equal-gap-and-defect/7B274AACAF3E385DE84825B5A0532BA7info: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:RCAAP2023-07-21T12:54:21Zoai:repositorium.sdum.uminho.pt:1822/79996Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:53:52.177760Repositório 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 Injective linear transformations with equal gap and defect
title Injective linear transformations with equal gap and defect
spellingShingle Injective linear transformations with equal gap and defect
Araújo, C. Mendes
ideals
Green's relations
Injective linear transformations
Quasiresiduals
Ciências Naturais::Matemáticas
Science & Technology
title_short Injective linear transformations with equal gap and defect
title_full Injective linear transformations with equal gap and defect
title_fullStr Injective linear transformations with equal gap and defect
title_full_unstemmed Injective linear transformations with equal gap and defect
title_sort Injective linear transformations with equal gap and defect
author Araújo, C. Mendes
author_facet Araújo, C. Mendes
Gonçalves, Suzana Mendes
author_role author
author2 Gonçalves, Suzana Mendes
author2_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Araújo, C. Mendes
Gonçalves, Suzana Mendes
dc.subject.por.fl_str_mv ideals
Green's relations
Injective linear transformations
Quasiresiduals
Ciências Naturais::Matemáticas
Science & Technology
topic ideals
Green's relations
Injective linear transformations
Quasiresiduals
Ciências Naturais::Matemáticas
Science & Technology
description Suppose V is an infinite-dimensional vector space over a field F and let I(V) denote the inverse semigroup of all injective partial linear transformations on V. Given ß in I(V), we denote the domain and the range of ß by dom ß and im ß, respectively, and we call the cardinals g(ß)=codim(domß) and d(ß)=codim(imß) the `gap' and the `defect' of ß, respectively. In this paper, we study the semigroup A(V) of all injective partial linear transformations with equal gap and defect, and characterise Green's relations and ideals in A(V). This is analogous to work by Sanwong and Sullivan in 2009 on a similarly-defined semigroup for the set case, but we show that these semigroups are never isomorphic.
publishDate 2022
dc.date.none.fl_str_mv 2022-02
2022-02-01T00:00:00Z
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/1822/79996
url https://hdl.handle.net/1822/79996
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Mendes Araújo, C., & Mendes-Gonçalves, S. (2022). Injective linear transformations with equal gap and defect. Bulletin of the Australian Mathematical Society, 105(1), 106-116. doi:10.1017/S0004972721000344
0004-9727
1755-1633
10.1017/S0004972721000344
https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/abs/injective-linear-transformations-with-equal-gap-and-defect/7B274AACAF3E385DE84825B5A0532BA7
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 Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
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
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
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