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On the Structure of the Irreducible Polynomials Over Local Fields

✍ Scribed by N. Popescu; A. Zaharescu

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
695 KB
Volume
52
Category
Article
ISSN
0022-314X

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✦ Synopsis

The paper is concerned with the structure of irreducible polynomials in one variable over a local field ((K, v)). The main achievement is the definition of a system (P(f)) of invariant factors for each monic irreducible polynomial (f \in K[X]). It is proved that these invariants are characteristic, i.e., by using invariants we may describe the set of irreducible polynomials over a local field. 1995 Academic Press. Inc.

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Let T n (x, a) Κ¦ GF(q)[x] be a Dickson polynomial over the finite field GF(q) of either the first kind or the second kind of degree n in the indeterminate x and with parameter a. We give a complete description of the factorization of T n (x, a) over GF(q).