A simple proof of a generalization of eisenstein's irreducibility criterion

We present a simple proof of Königsberg's Criterion, [K] p.69 and also present families of irreducible polynomials over some fields. In particular, if (n, h) = 1, ao….., an-1 ϵ Z = ring of integers and p is a primer not dividing ao,  then f (x) = xn - ph(ao+a1+…+an-1Xn-1) is irredudible over th...

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Autores:
Allan, Nelo
Tipo de recurso:
Article of journal
Fecha de publicación:
1987
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/43126
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/43126
http://bdigital.unal.edu.co/33224/
Palabra clave:
5 Ciencias naturales y matemáticas / Science
51 Matemáticas / Mathematics
Königsberg's criterion
polynomials
integers
rational numbers
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Allan, Nelo481c6c34-8c37-402a-98c9-16fd4407f5773002019-06-28T11:35:28Z2019-06-28T11:35:28Z1987https://repositorio.unal.edu.co/handle/unal/43126http://bdigital.unal.edu.co/33224/We present a simple proof of Königsberg's Criterion, [K] p.69 and also present families of irreducible polynomials over some fields. In particular, if (n, h) = 1, ao….., an-1 ϵ Z = ring of integers and p is a primer not dividing ao,  then f (x) = xn - ph(ao+a1+…+an-1Xn-1) is irredudible over the rationals. Also if k is any field, then [Formula Matemática].application/pdfspaUniversidad Nacuional de Colombia; Sociedad Colombiana de matemáticashttp://revistas.unal.edu.co/index.php/recolma/article/view/33020Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasRevista Colombiana de Matemáticas; Vol. 21, núm. 1 (1987); 141-146 0034-7426Allan, Nelo (1987) A simple proof of a generalization of eisenstein's irreducibility criterion. Revista Colombiana de Matemáticas; Vol. 21, núm. 1 (1987); 141-146 0034-7426 .5 Ciencias naturales y matemáticas / Science51 Matemáticas / MathematicsKönigsberg's criterionpolynomialsintegersrational numbersA simple proof of a generalization of eisenstein's irreducibility criterionArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL33020-122381-1-PB.pdfapplication/pdf1566632https://repositorio.unal.edu.co/bitstream/unal/43126/1/33020-122381-1-PB.pdfdf9c7967f1faedf87235b32755eef9d5MD51THUMBNAIL33020-122381-1-PB.pdf.jpg33020-122381-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg6408https://repositorio.unal.edu.co/bitstream/unal/43126/2/33020-122381-1-PB.pdf.jpgbb2d79c119179c1ebc9fd47a86008688MD52unal/43126oai:repositorio.unal.edu.co:unal/431262023-02-11 23:04:02.935Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv A simple proof of a generalization of eisenstein's irreducibility criterion
title A simple proof of a generalization of eisenstein's irreducibility criterion
spellingShingle A simple proof of a generalization of eisenstein's irreducibility criterion
5 Ciencias naturales y matemáticas / Science
51 Matemáticas / Mathematics
Königsberg's criterion
polynomials
integers
rational numbers
title_short A simple proof of a generalization of eisenstein's irreducibility criterion
title_full A simple proof of a generalization of eisenstein's irreducibility criterion
title_fullStr A simple proof of a generalization of eisenstein's irreducibility criterion
title_full_unstemmed A simple proof of a generalization of eisenstein's irreducibility criterion
title_sort A simple proof of a generalization of eisenstein's irreducibility criterion
dc.creator.fl_str_mv Allan, Nelo
dc.contributor.author.spa.fl_str_mv Allan, Nelo
dc.subject.ddc.spa.fl_str_mv 5 Ciencias naturales y matemáticas / Science
51 Matemáticas / Mathematics
topic 5 Ciencias naturales y matemáticas / Science
51 Matemáticas / Mathematics
Königsberg's criterion
polynomials
integers
rational numbers
dc.subject.proposal.spa.fl_str_mv Königsberg's criterion
polynomials
integers
rational numbers
description We present a simple proof of Königsberg's Criterion, [K] p.69 and also present families of irreducible polynomials over some fields. In particular, if (n, h) = 1, ao….., an-1 ϵ Z = ring of integers and p is a primer not dividing ao,  then f (x) = xn - ph(ao+a1+…+an-1Xn-1) is irredudible over the rationals. Also if k is any field, then [Formula Matemática].
publishDate 1987
dc.date.issued.spa.fl_str_mv 1987
dc.date.accessioned.spa.fl_str_mv 2019-06-28T11:35:28Z
dc.date.available.spa.fl_str_mv 2019-06-28T11:35:28Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.type.content.spa.fl_str_mv Text
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format http://purl.org/coar/resource_type/c_6501
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dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/43126
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/33224/
url https://repositorio.unal.edu.co/handle/unal/43126
http://bdigital.unal.edu.co/33224/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.spa.fl_str_mv http://revistas.unal.edu.co/index.php/recolma/article/view/33020
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas
Revista Colombiana de Matemáticas
dc.relation.ispartofseries.none.fl_str_mv Revista Colombiana de Matemáticas; Vol. 21, núm. 1 (1987); 141-146 0034-7426
dc.relation.references.spa.fl_str_mv Allan, Nelo (1987) A simple proof of a generalization of eisenstein's irreducibility criterion. Revista Colombiana de Matemáticas; Vol. 21, núm. 1 (1987); 141-146 0034-7426 .
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/43126/1/33020-122381-1-PB.pdf
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repository.name.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
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