Shahrood University of TechnologyJournal of Algebraic Systems2345-512811220240101A CLASSIFICATION OF EXTENSIONS GENERATED BY A ROOT OF AN EISENSTEIN-DUMAS POLYNOMIAL8391273210.22044/jas.2022.11808.1603ENَAzadeh NiksereshtDepartment of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran.0000-0002-3892-9881Journal Article20220407It 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.https://jas.shahroodut.ac.ir/article_2732_348fbdd2888fbfecbecd8c5bf762901d.pdf