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On the structure of the irreducible polynomials over local fields. (English) Zbl 0838.11078

A field \(K\) is called local if it is complete relative to a rank one and discrete valuation \(v\). The authors examine the structure of irreducible polynomials in one variable over \(K\). They introduce the definition of a system \(P(f)\) of invariant factors for each monic irreducible polynomial \(f\) in \(K[X]\). They prove that these invariants are characteristic. They apply their results to understand the extension of the natural valuation of a local field \(K\) to the field given by the considered polynomial.

MSC:

11S05 Polynomials
12F05 Algebraic field extensions
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