Publié-e

1987-01-01

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

Mots-clés :

Königsberg's criterion, polynomials, integers, rational numbers (es)

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Auteurs-es

  • Nelo D. Allan Universidade Estadual de Campinas

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].

Comment citer

APA

Allan, N. D. (1987). A simple proof of a generalization of Eisenstein’s irreducibility criterion. Revista Colombiana de Matemáticas, 21(1), 141–146. https://revistas.unal.edu.co/index.php/recolma/article/view/33020

ACM

[1]
Allan, N.D. 1987. A simple proof of a generalization of Eisenstein’s irreducibility criterion. Revista Colombiana de Matemáticas. 21, 1 (janv. 1987), 141–146.

ACS

(1)
Allan, N. D. A simple proof of a generalization of Eisenstein’s irreducibility criterion. rev.colomb.mat 1987, 21, 141-146.

ABNT

ALLAN, N. D. A simple proof of a generalization of Eisenstein’s irreducibility criterion. Revista Colombiana de Matemáticas, [S. l.], v. 21, n. 1, p. 141–146, 1987. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/33020. Acesso em: 22 janv. 2025.

Chicago

Allan, Nelo D. 1987. « A simple proof of a generalization of Eisenstein’s irreducibility criterion ». Revista Colombiana De Matemáticas 21 (1):141-46. https://revistas.unal.edu.co/index.php/recolma/article/view/33020.

Harvard

Allan, N. D. (1987) « A simple proof of a generalization of Eisenstein’s irreducibility criterion », Revista Colombiana de Matemáticas, 21(1), p. 141–146. Disponible à: https://revistas.unal.edu.co/index.php/recolma/article/view/33020 (Consulté le: 22 janvier 2025).

IEEE

[1]
N. D. Allan, « A simple proof of a generalization of Eisenstein’s irreducibility criterion », rev.colomb.mat, vol. 21, nᵒ 1, p. 141–146, janv. 1987.

MLA

Allan, N. D. « A simple proof of a generalization of Eisenstein’s irreducibility criterion ». Revista Colombiana de Matemáticas, vol. 21, nᵒ 1, janvier 1987, p. 141-6, https://revistas.unal.edu.co/index.php/recolma/article/view/33020.

Turabian

Allan, Nelo D. « A simple proof of a generalization of Eisenstein’s irreducibility criterion ». Revista Colombiana de Matemáticas 21, no. 1 (janvier 1, 1987): 141–146. Consulté le janvier 22, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/33020.

Vancouver

1.
Allan ND. A simple proof of a generalization of Eisenstein’s irreducibility criterion. rev.colomb.mat [Internet]. 1 janv. 1987 [cité 22 janv. 2025];21(1):141-6. Disponible à: https://revistas.unal.edu.co/index.php/recolma/article/view/33020

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