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...
- 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
| 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]. |
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