%0 Journal Article
%T A CLASSIFICATION OF EXTENSIONS GENERATED BY A ROOT OF AN EISENSTEIN-DUMAS POLYNOMIAL
%J Journal of Algebraic Systems
%I Shahrood University of Technology
%Z 2345-5128
%A Nikseresht, َAzadeh
%D 2024
%\ 01/01/2024
%V 11
%N 2
%P 83-91
%! A CLASSIFICATION OF EXTENSIONS GENERATED BY A ROOT OF AN EISENSTEIN-DUMAS POLYNOMIAL
%K Algebraic field extensions
%K valued fields
%K polynomials in general fields
%R 10.22044/jas.2022.11808.1603
%X It is known that for a discrete valuation v of a field K with value group Z, an valued extension field (K′, v′) of (K, v) is generated by a root of an Eisenstein polynomial with respect to v having coefficients in K if and only if the extension (K′, v′)/(K, v) is totally ramified. The aim of this paper is to present the analogue of this result for valued field extensions generated by a root of an Eisenstein-Dumas polynomial with respect to a more general valuation (which is not necessarily discrete). This leads to classify such algebraic extensions of valued fields.
%U https://jas.shahroodut.ac.ir/article_2732_348fbdd2888fbfecbecd8c5bf762901d.pdf