Popescu, Nicolae; Zaharescu, Alexandru On the structure of the irreducible polynomials over local fields. (English) Zbl 0838.11078 J. Number Theory 52, No. 1, 98-118 (1995). 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. Reviewer: J.N.Mordeson (Omaha) Cited in 12 ReviewsCited in 37 Documents MSC: 11S05 Polynomials 12F05 Algebraic field extensions Keywords:irreducible polynomials over local fields; extension of natural valuation; system of invariant factors PDFBibTeX XMLCite \textit{N. Popescu} and \textit{A. Zaharescu}, J. Number Theory 52, No. 1, 98--118 (1995; Zbl 0838.11078) Full Text: DOI