Partial orders on transformation semigroups

Detalhes bibliográficos
Autor(a) principal: Smith, M. Paula Marques
Data de Publicação: 2003
Outros Autores: Sullivan, R. P.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/7451
Resumo: In 1986, Kowol and Mitsch studied properties of the so-called 'natural partial order' less than or equal to on T(X), the total transformation semigroup defined on a set X. In particular, they determined when two total transformations are related under this order, and they described the minimal and maximal elements of (T(X), less than or equal to). In this paper, we extend that work to the semigroup P(X) of all partial transformations of X, compare less than or equal to with another 'natural' partial order on P(X), characterise the meet and join of these two orders, and determine the minimal and maximal elements of P(X) with respect to each order.
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spelling Partial orders on transformation semigroupsNatural partial orderTransformation semigroupScience & TechnologyIn 1986, Kowol and Mitsch studied properties of the so-called 'natural partial order' less than or equal to on T(X), the total transformation semigroup defined on a set X. In particular, they determined when two total transformations are related under this order, and they described the minimal and maximal elements of (T(X), less than or equal to). In this paper, we extend that work to the semigroup P(X) of all partial transformations of X, compare less than or equal to with another 'natural' partial order on P(X), characterise the meet and join of these two orders, and determine the minimal and maximal elements of P(X) with respect to each order.Centro de Matemática da Universidade do Minho.Fundação para a Ciência e a Tecnologia (FCT).SpringerUniversidade do MinhoSmith, M. Paula MarquesSullivan, R. P.20032003-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/7451eng"Monatshefte für Mathematik". ISSN 0026-9255. 140:2 (2003) 103-118.0026-925510.1007/s00605-002-0546-4www.springerlink.comhttp://springerlink.com/content/k2f56v7nu7d5ga2l/info: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:RCAAP2023-07-21T12:37:51Zoai:repositorium.sdum.uminho.pt:1822/7451Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:34:11.732486Repositório 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 Partial orders on transformation semigroups
title Partial orders on transformation semigroups
spellingShingle Partial orders on transformation semigroups
Smith, M. Paula Marques
Natural partial order
Transformation semigroup
Science & Technology
title_short Partial orders on transformation semigroups
title_full Partial orders on transformation semigroups
title_fullStr Partial orders on transformation semigroups
title_full_unstemmed Partial orders on transformation semigroups
title_sort Partial orders on transformation semigroups
author Smith, M. Paula Marques
author_facet Smith, M. Paula Marques
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 Smith, M. Paula Marques
Sullivan, R. P.
dc.subject.por.fl_str_mv Natural partial order
Transformation semigroup
Science & Technology
topic Natural partial order
Transformation semigroup
Science & Technology
description In 1986, Kowol and Mitsch studied properties of the so-called 'natural partial order' less than or equal to on T(X), the total transformation semigroup defined on a set X. In particular, they determined when two total transformations are related under this order, and they described the minimal and maximal elements of (T(X), less than or equal to). In this paper, we extend that work to the semigroup P(X) of all partial transformations of X, compare less than or equal to with another 'natural' partial order on P(X), characterise the meet and join of these two orders, and determine the minimal and maximal elements of P(X) with respect to each order.
publishDate 2003
dc.date.none.fl_str_mv 2003
2003-01-01T00:00:00Z
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 http://hdl.handle.net/1822/7451
url http://hdl.handle.net/1822/7451
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv "Monatshefte für Mathematik". ISSN 0026-9255. 140:2 (2003) 103-118.
0026-9255
10.1007/s00605-002-0546-4
www.springerlink.com
http://springerlink.com/content/k2f56v7nu7d5ga2l/
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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