Semi-Heyting Algebras and Identities of Associative Type

Autores
Cornejo, Juan Manuel; Sankappanavar, Hanamantagouda P.
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
An algebra A = ⟨A, ∨, ∧, →, 0, 1⟩ is a semi-Heyting algebra if ⟨A, ∨, ∧, 0, 1⟩ is a bounded lattice, and it satisfies the identities: x ∧ (x → y) ≈ x ∧ y, x ∧ (y → z) ≈ x ∧ [(x ∧ y) → (x ∧ z)], and x → x ≈ 1. ℋ denotes the variety of semi-Heyting algebras. Semi-Heyting algebras were introduced by the second author as an abstraction from Heyting algebras. They share several important properties with Heyting algebras. An identity of associative type of length 3 is a groupoid identity, both sides of which contain the same three (distinct) variables that occur in any order and that are grouped in one of the two (obvious) ways. A subvariety of ℋ is of associative type of length 3 if it is defined by a single identity of associative type of length 3. In this paper we describe all the distinct subvarieties of the variety ℋ of asociative type of length 3. Our main result shows that there are 3 such subvarities of ℋ.
Fil: Cornejo, Juan Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Fil: Sankappanavar, Hanamantagouda P.. State University of New York. Department of Mathematics; Estados Unidos
Materia
SEMI-HEYTING ALGEBRA
HEYTING ALGEBRA
IDENTITY OF ASSOCIATIVE TYPE
SUBVARIETY OF ASSOCIATIVE TYPE
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/137819
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Semi-Heyting Algebras and Identities of Associative TypeCornejo, Juan ManuelSankappanavar, Hanamantagouda P.SEMI-HEYTING ALGEBRAHEYTING ALGEBRAIDENTITY OF ASSOCIATIVE TYPESUBVARIETY OF ASSOCIATIVE TYPEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1An algebra A = ⟨A, ∨, ∧, →, 0, 1⟩ is a semi-Heyting algebra if ⟨A, ∨, ∧, 0, 1⟩ is a bounded lattice, and it satisfies the identities: x ∧ (x → y) ≈ x ∧ y, x ∧ (y → z) ≈ x ∧ [(x ∧ y) → (x ∧ z)], and x → x ≈ 1. ℋ denotes the variety of semi-Heyting algebras. Semi-Heyting algebras were introduced by the second author as an abstraction from Heyting algebras. They share several important properties with Heyting algebras. An identity of associative type of length 3 is a groupoid identity, both sides of which contain the same three (distinct) variables that occur in any order and that are grouped in one of the two (obvious) ways. A subvariety of ℋ is of associative type of length 3 if it is defined by a single identity of associative type of length 3. In this paper we describe all the distinct subvarieties of the variety ℋ of asociative type of length 3. Our main result shows that there are 3 such subvarities of ℋ.Fil: Cornejo, Juan Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Sankappanavar, Hanamantagouda P.. State University of New York. Department of Mathematics; Estados UnidosUniversity of Lodz2019-06-30info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/137819Cornejo, Juan Manuel; Sankappanavar, Hanamantagouda P.; Semi-Heyting Algebras and Identities of Associative Type; University of Lodz; Bulletin Of The Section Of Logic; 48; 2; 30-6-2019; 117-1350138-0680CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://czasopisma.uni.lodz.pl/bulletin/article/view/5436info:eu-repo/semantics/altIdentifier/doi/10.18778/0138-0680.48.2.03info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T10:26:11Zoai:ri.conicet.gov.ar:11336/137819instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-11-05 10:26:11.99CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Semi-Heyting Algebras and Identities of Associative Type
title Semi-Heyting Algebras and Identities of Associative Type
spellingShingle Semi-Heyting Algebras and Identities of Associative Type
Cornejo, Juan Manuel
SEMI-HEYTING ALGEBRA
HEYTING ALGEBRA
IDENTITY OF ASSOCIATIVE TYPE
SUBVARIETY OF ASSOCIATIVE TYPE
title_short Semi-Heyting Algebras and Identities of Associative Type
title_full Semi-Heyting Algebras and Identities of Associative Type
title_fullStr Semi-Heyting Algebras and Identities of Associative Type
title_full_unstemmed Semi-Heyting Algebras and Identities of Associative Type
title_sort Semi-Heyting Algebras and Identities of Associative Type
dc.creator.none.fl_str_mv Cornejo, Juan Manuel
Sankappanavar, Hanamantagouda P.
author Cornejo, Juan Manuel
author_facet Cornejo, Juan Manuel
Sankappanavar, Hanamantagouda P.
author_role author
author2 Sankappanavar, Hanamantagouda P.
author2_role author
dc.subject.none.fl_str_mv SEMI-HEYTING ALGEBRA
HEYTING ALGEBRA
IDENTITY OF ASSOCIATIVE TYPE
SUBVARIETY OF ASSOCIATIVE TYPE
topic SEMI-HEYTING ALGEBRA
HEYTING ALGEBRA
IDENTITY OF ASSOCIATIVE TYPE
SUBVARIETY OF ASSOCIATIVE TYPE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv An algebra A = ⟨A, ∨, ∧, →, 0, 1⟩ is a semi-Heyting algebra if ⟨A, ∨, ∧, 0, 1⟩ is a bounded lattice, and it satisfies the identities: x ∧ (x → y) ≈ x ∧ y, x ∧ (y → z) ≈ x ∧ [(x ∧ y) → (x ∧ z)], and x → x ≈ 1. ℋ denotes the variety of semi-Heyting algebras. Semi-Heyting algebras were introduced by the second author as an abstraction from Heyting algebras. They share several important properties with Heyting algebras. An identity of associative type of length 3 is a groupoid identity, both sides of which contain the same three (distinct) variables that occur in any order and that are grouped in one of the two (obvious) ways. A subvariety of ℋ is of associative type of length 3 if it is defined by a single identity of associative type of length 3. In this paper we describe all the distinct subvarieties of the variety ℋ of asociative type of length 3. Our main result shows that there are 3 such subvarities of ℋ.
Fil: Cornejo, Juan Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Fil: Sankappanavar, Hanamantagouda P.. State University of New York. Department of Mathematics; Estados Unidos
description An algebra A = ⟨A, ∨, ∧, →, 0, 1⟩ is a semi-Heyting algebra if ⟨A, ∨, ∧, 0, 1⟩ is a bounded lattice, and it satisfies the identities: x ∧ (x → y) ≈ x ∧ y, x ∧ (y → z) ≈ x ∧ [(x ∧ y) → (x ∧ z)], and x → x ≈ 1. ℋ denotes the variety of semi-Heyting algebras. Semi-Heyting algebras were introduced by the second author as an abstraction from Heyting algebras. They share several important properties with Heyting algebras. An identity of associative type of length 3 is a groupoid identity, both sides of which contain the same three (distinct) variables that occur in any order and that are grouped in one of the two (obvious) ways. A subvariety of ℋ is of associative type of length 3 if it is defined by a single identity of associative type of length 3. In this paper we describe all the distinct subvarieties of the variety ℋ of asociative type of length 3. Our main result shows that there are 3 such subvarities of ℋ.
publishDate 2019
dc.date.none.fl_str_mv 2019-06-30
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/137819
Cornejo, Juan Manuel; Sankappanavar, Hanamantagouda P.; Semi-Heyting Algebras and Identities of Associative Type; University of Lodz; Bulletin Of The Section Of Logic; 48; 2; 30-6-2019; 117-135
0138-0680
CONICET Digital
CONICET
url http://hdl.handle.net/11336/137819
identifier_str_mv Cornejo, Juan Manuel; Sankappanavar, Hanamantagouda P.; Semi-Heyting Algebras and Identities of Associative Type; University of Lodz; Bulletin Of The Section Of Logic; 48; 2; 30-6-2019; 117-135
0138-0680
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://czasopisma.uni.lodz.pl/bulletin/article/view/5436
info:eu-repo/semantics/altIdentifier/doi/10.18778/0138-0680.48.2.03
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv University of Lodz
publisher.none.fl_str_mv University of Lodz
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.087074

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