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Eisenstein's Criteria for Absolute Irreducibility Over a Finite Field

Published online by Cambridge University Press:  20 November 2018

Kenneth S. Williams
Kenneth S. Williams*
Affiliation:
Carleton University, Ottawa
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Let p denote a prime and n a positive integer. Write q = pn and let kq denote the Galois field with q elements. The unique factorization domain of polynomials in m(≤ 2) indeterminâtes x1,…, xq with coefficients in k is denoted by kq [x,…, xm. It is the purpose of this note to prove the foliowing generalization of Eisenstein's irreducibility criteria and to point out some of its consequences.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 5 , December 1966 , pp. 575 - 580
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Birch, B.J. and Lewis, D.J., p-adic forms. J. Ind. Math. Soc, 23 (1959), pages 11-32.Google Scholar
2. Van der Waerden, B.L., Modern Algebra. Fred. Ungar Publish. Co. N.Y., (1953), page 74.Google Scholar