Equivalence between varieties of square root rings and Boolean algebras with a distinguished automorphism

Autores
Díaz Varela, José Patricio
Año de publicación
2006
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we study the variety R2 of square root rings, that is, commutative rings with unit, of characteristic two, with the square root as an additional operation. We prove that this variety is generated by the finite Galois fields GF ( 2k ) and we establish an equivalence between R2 and the variety BA δ of Boolean algebras with a distinguished automorphism. Via this equivalence, we will be able to obtain properties of R2 from the results proved in [M. Abad, J.P. Díaz Varela, M. Zander, Boolean algebras with a distinguished automorphism, Rep. Math. Logic 37 (2003) 101-112].
Fil: Díaz Varela, José Patricio. 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
Materia
BOOLEAN ALGEBRAS
COMMUTATIVE RINGS
FINITE FIELDS
FROBENIUS AUTOMORPHISM
INTERPRETATIONS
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:11336/96058
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/96058
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Equivalence between varieties of square root rings and Boolean algebras with a distinguished automorphismDíaz Varela, José PatricioBOOLEAN ALGEBRASCOMMUTATIVE RINGSFINITE FIELDSFROBENIUS AUTOMORPHISMINTERPRETATIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we study the variety R2 of square root rings, that is, commutative rings with unit, of characteristic two, with the square root as an additional operation. We prove that this variety is generated by the finite Galois fields GF ( 2k ) and we establish an equivalence between R2 and the variety BA δ of Boolean algebras with a distinguished automorphism. Via this equivalence, we will be able to obtain properties of R2 from the results proved in [M. Abad, J.P. Díaz Varela, M. Zander, Boolean algebras with a distinguished automorphism, Rep. Math. Logic 37 (2003) 101-112].Fil: Díaz Varela, José Patricio. 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; ArgentinaAcademic Press Inc Elsevier Science2006-05info: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/11336/96058Díaz Varela, José Patricio; Equivalence between varieties of square root rings and Boolean algebras with a distinguished automorphism; Academic Press Inc Elsevier Science; Journal of Algebra; 299; 1; 5-2006; 190-1970021-8693CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2006.02.017info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0021869306001165info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:45:09Zoai:ri.conicet.gov.ar:11336/96058instacron: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:34982025-09-29 10:45:09.345CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Equivalence between varieties of square root rings and Boolean algebras with a distinguished automorphism
title Equivalence between varieties of square root rings and Boolean algebras with a distinguished automorphism
spellingShingle Equivalence between varieties of square root rings and Boolean algebras with a distinguished automorphism
Díaz Varela, José Patricio
BOOLEAN ALGEBRAS
COMMUTATIVE RINGS
FINITE FIELDS
FROBENIUS AUTOMORPHISM
INTERPRETATIONS
title_short Equivalence between varieties of square root rings and Boolean algebras with a distinguished automorphism
title_full Equivalence between varieties of square root rings and Boolean algebras with a distinguished automorphism
title_fullStr Equivalence between varieties of square root rings and Boolean algebras with a distinguished automorphism
title_full_unstemmed Equivalence between varieties of square root rings and Boolean algebras with a distinguished automorphism
title_sort Equivalence between varieties of square root rings and Boolean algebras with a distinguished automorphism
dc.creator.none.fl_str_mv Díaz Varela, José Patricio
author Díaz Varela, José Patricio
author_facet Díaz Varela, José Patricio
author_role author
dc.subject.none.fl_str_mv BOOLEAN ALGEBRAS
COMMUTATIVE RINGS
FINITE FIELDS
FROBENIUS AUTOMORPHISM
INTERPRETATIONS
topic BOOLEAN ALGEBRAS
COMMUTATIVE RINGS
FINITE FIELDS
FROBENIUS AUTOMORPHISM
INTERPRETATIONS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we study the variety R2 of square root rings, that is, commutative rings with unit, of characteristic two, with the square root as an additional operation. We prove that this variety is generated by the finite Galois fields GF ( 2k ) and we establish an equivalence between R2 and the variety BA δ of Boolean algebras with a distinguished automorphism. Via this equivalence, we will be able to obtain properties of R2 from the results proved in [M. Abad, J.P. Díaz Varela, M. Zander, Boolean algebras with a distinguished automorphism, Rep. Math. Logic 37 (2003) 101-112].
Fil: Díaz Varela, José Patricio. 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
description In this paper we study the variety R2 of square root rings, that is, commutative rings with unit, of characteristic two, with the square root as an additional operation. We prove that this variety is generated by the finite Galois fields GF ( 2k ) and we establish an equivalence between R2 and the variety BA δ of Boolean algebras with a distinguished automorphism. Via this equivalence, we will be able to obtain properties of R2 from the results proved in [M. Abad, J.P. Díaz Varela, M. Zander, Boolean algebras with a distinguished automorphism, Rep. Math. Logic 37 (2003) 101-112].
publishDate 2006
dc.date.none.fl_str_mv 2006-05
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/11336/96058
Díaz Varela, José Patricio; Equivalence between varieties of square root rings and Boolean algebras with a distinguished automorphism; Academic Press Inc Elsevier Science; Journal of Algebra; 299; 1; 5-2006; 190-197
0021-8693
CONICET Digital
CONICET
url http://hdl.handle.net/11336/96058
identifier_str_mv Díaz Varela, José Patricio; Equivalence between varieties of square root rings and Boolean algebras with a distinguished automorphism; Academic Press Inc Elsevier Science; Journal of Algebra; 299; 1; 5-2006; 190-197
0021-8693
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2006.02.017
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0021869306001165
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 Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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 13.070432

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