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

Nelo D. Allan

Published

1987-01-01

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

Keywords:

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

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Authors

Nelo D. Allan Universidade Estadual de Campinas

Abstract (es)

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, a_o….., a_n-1 ϵ Z = ring of integers and p is a primer not dividing a_o, then f (x) = xⁿ - p^h(a_o+a₁+…+a_n-1X^n-1) is irredudible over the rationals. Also if k is any field, then [Formula Matemática].

How to Cite

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 (Jan. 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: 13 mar. 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), pp. 141–146. Available at: https://revistas.unal.edu.co/index.php/recolma/article/view/33020 (Accessed: 13 March 2025).

IEEE

[1]

N. D. Allan, “A simple proof of a generalization of Eisenstein’s irreducibility criterion”, rev.colomb.mat, vol. 21, no. 1, pp. 141–146, Jan. 1987.

MLA

Allan, N. D. “A simple proof of a generalization of Eisenstein’s irreducibility criterion”. Revista Colombiana de Matemáticas, vol. 21, no. 1, Jan. 1987, pp. 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 (January 1, 1987): 141–146. Accessed March 13, 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]. 1987 Jan. 1 [cited 2025 Mar. 13];21(1):141-6. Available from: https://revistas.unal.edu.co/index.php/recolma/article/view/33020