Why Eisenstein Proved the Eisenstein Criterion and Why Schönemann Discovered It First

@article{Cox2011WhyEP,
  title={Why Eisenstein Proved the Eisenstein Criterion and Why Sch{\"o}nemann Discovered It First},
  author={D. Cox},
  journal={The American Mathematical Monthly},
  year={2011},
  volume={118},
  pages={21 - 3}
}
  • D. Cox
  • Published 2011
  • Mathematics, Computer Science
  • The American Mathematical Monthly
Abstract This article explores the history of the Eisenstein irreducibility criterion and explains how Theodor Schönemann discovered this criterion before Eisenstein. Both were inspired by Gauss's Disquisitiones Arithmeticae, though they took very different routes to their discoveries. The article will discuss a variety of topics from 19th-century number theory, including Gauss's lemma, finite fields, the lemniscate, elliptic integrals, abelian groups, the Gaussian integers, and Hensel's lemma. 
A Generalization of the Eisenstein–Dumas–Schönemann Irreducibility Criterion
Gauss’ lemma and valuation theory
Several Proofs of the Irreducibility of the Cyclotomic Polynomials
Eisenstein's criterion, Fermat's last theorem, and a conjecture on powerful numbers
On shifted Eisenstein polynomials
On the number of Eisenstein polynomials of bounded height
Geometric constructibility of cyclic polygons and a limit theorem
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References

SHOWING 1-10 OF 54 REFERENCES
Abel's Theorem on the Lemniscate
History of the Theory of Numbers
History of the Theory of Numbers
Galois Theory
The Arithmetic-Geometric Mean of Gauss
Primes of the form x2 + ny2
Mathematische Werke
MATH
...
1
2
3
4
5
...