%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, ŮŽAzadeh %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