A mild generalization of Eisenstein’s criterion-Reference-Cited by-同舟云学术

A mild generalization of Eisenstein’s criterion

Published:2012-08-24 Issue:4 Volume:141 Page:1159-1160
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Weintraub Steven

Abstract

We state and prove a mild generalization of Eisenstein’s Criterion for a polynomial to be irreducible, correcting an error that Eisenstein made himself.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2013-141-04/S0002-9939-2012-10880-9/S0002-9939-2012-10880-9.pdf

Reference6 articles.

1. Why Eisenstein proved the Eisenstein criterion and why Schönemann discovered it first;Cox, David A.;Normat,2009

2. Eisenstein, F. G. M., Über die Irreductibilität und einige andere Eigenschaften der Gleichung, von welcher die Theilung der ganzen Lemniscate abhängt, J. reine angew. Math. 39 (1850), 160-179.

3. Galois, E., Mémoire sur les conditions de résolubilité des équations par radicaux, J. Math. Pure Appl. 11 (1846), 381-444.

4. Gauss, C. F., Disquisitiones Arithmeticae, Leipzig, 1801.

5. Kronecker, L., Beweis dass für jede Primzahl 𝑝 die Gleichung 1+𝑥+…+𝑥^{𝑝-1}=0 irreductibel ist, J. reine angew. Math. 29 (1845), 280.

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