On difunctionality of class relations
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10316/89450 https://doi.org/10.1007/s00012-020-00651-z |
Resumo: | For a given variety V of algebras, we define a class relation to be a binary relation R ⊆ S^2 which is of the form R = S^2 ∩ K for some congruence class K on A^2, where A is an algebra in V such that S ⊆ A. In this paper we study the following property of V: every reflexive class relation is an equivalence relation. In particular, we obtain equivalent characterizations of this property analogous to well-known equivalent characterizations of congruence-permutable varieties. This property determines a Mal’tsev condition on the variety and in a suitable sense, it is a join of Chajda’s egg-box property as well as Duda’s direct decomposability of congruence classes. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
spelling |
On difunctionality of class relationsClass relations, Congruence permutability, Congruence distributivity, Congruence modularity, Directly decomposable congruence classes, Difunctionality, Egg-box property, Mal’tsev condition, Mal’tsev variety, Shifting lemma.For a given variety V of algebras, we define a class relation to be a binary relation R ⊆ S^2 which is of the form R = S^2 ∩ K for some congruence class K on A^2, where A is an algebra in V such that S ⊆ A. In this paper we study the following property of V: every reflexive class relation is an equivalence relation. In particular, we obtain equivalent characterizations of this property analogous to well-known equivalent characterizations of congruence-permutable varieties. This property determines a Mal’tsev condition on the variety and in a suitable sense, it is a join of Chajda’s egg-box property as well as Duda’s direct decomposability of congruence classes.Springer Verlag2020info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/89450http://hdl.handle.net/10316/89450https://doi.org/10.1007/s00012-020-00651-zenghttps://link.springer.com/article/10.1007/s00012-020-00651-zHoefnagel, MichaelJanelidze, ZurabRodelo, Dianainfo: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:RCAAP2022-05-25T06:20:58Zoai:estudogeral.uc.pt:10316/89450Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:09:45.626037Repositório 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 |
On difunctionality of class relations |
title |
On difunctionality of class relations |
spellingShingle |
On difunctionality of class relations Hoefnagel, Michael Class relations, Congruence permutability, Congruence distributivity, Congruence modularity, Directly decomposable congruence classes, Difunctionality, Egg-box property, Mal’tsev condition, Mal’tsev variety, Shifting lemma. |
title_short |
On difunctionality of class relations |
title_full |
On difunctionality of class relations |
title_fullStr |
On difunctionality of class relations |
title_full_unstemmed |
On difunctionality of class relations |
title_sort |
On difunctionality of class relations |
author |
Hoefnagel, Michael |
author_facet |
Hoefnagel, Michael Janelidze, Zurab Rodelo, Diana |
author_role |
author |
author2 |
Janelidze, Zurab Rodelo, Diana |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Hoefnagel, Michael Janelidze, Zurab Rodelo, Diana |
dc.subject.por.fl_str_mv |
Class relations, Congruence permutability, Congruence distributivity, Congruence modularity, Directly decomposable congruence classes, Difunctionality, Egg-box property, Mal’tsev condition, Mal’tsev variety, Shifting lemma. |
topic |
Class relations, Congruence permutability, Congruence distributivity, Congruence modularity, Directly decomposable congruence classes, Difunctionality, Egg-box property, Mal’tsev condition, Mal’tsev variety, Shifting lemma. |
description |
For a given variety V of algebras, we define a class relation to be a binary relation R ⊆ S^2 which is of the form R = S^2 ∩ K for some congruence class K on A^2, where A is an algebra in V such that S ⊆ A. In this paper we study the following property of V: every reflexive class relation is an equivalence relation. In particular, we obtain equivalent characterizations of this property analogous to well-known equivalent characterizations of congruence-permutable varieties. This property determines a Mal’tsev condition on the variety and in a suitable sense, it is a join of Chajda’s egg-box property as well as Duda’s direct decomposability of congruence classes. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020 |
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/10316/89450 http://hdl.handle.net/10316/89450 https://doi.org/10.1007/s00012-020-00651-z |
url |
http://hdl.handle.net/10316/89450 https://doi.org/10.1007/s00012-020-00651-z |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://link.springer.com/article/10.1007/s00012-020-00651-z |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Springer Verlag |
publisher.none.fl_str_mv |
Springer Verlag |
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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1799133992893546496 |