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...

Full description

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
Description
Summary: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].