A mild generalization of Eisenstein’s criterion
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- by Steven H. Weintraub PDF
- Proc. Amer. Math. Soc. 141 (2013), 1159-1160 Request permission
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.References
- David A. Cox, Why Eisenstein proved the Eisenstein criterion and why Schönemann discovered it first, Normat 57 (2009), no. 2, 49–73, 96. MR 2572615
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- Gauss, C. F., Disquisitiones Arithmeticae, Leipzig, 1801.
- Kronecker, L., Beweis dass für jede Primzahl $p$ die Gleichung $1+x+\ldots +x^{p-1}=0$ irreductibel ist, J. reine angew. Math. 29 (1845), 280.
- Schönemann, T. Von denjenigen Moduln, welche Potenzen von Primzahlen sind, J. reine angew. Math. 32 (1846), 93-105.
Additional Information
- Steven H. Weintraub
- Affiliation: Department of Mathematics, Lehigh University, Bethlehem, Pennsylvannia 18015-3174
- MR Author ID: 181515
- ORCID: 0000-0002-3290-363X
- Email: shw2@lehigh.edu
- Received by editor(s): November 3, 2010
- Received by editor(s) in revised form: August 12, 2011
- Published electronically: August 24, 2012
- Communicated by: Ken Ono
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 1159-1160
- MSC (2010): Primary 12E05; Secondary 01A55
- DOI: https://doi.org/10.1090/S0002-9939-2012-10880-9
- MathSciNet review: 3008863