A CLASSIFICATION OF EXTENSIONS GENERATED BY A ROOT OF AN EISENSTEIN-DUMAS POLYNOMIAL | ||
| Journal of Algebraic Systems | ||
| دوره 11، شماره 2، فروردین 2024، صفحه 83-91 اصل مقاله (131.07 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.11808.1603 | ||
| نویسنده | ||
| َAzadeh Nikseresht* | ||
| Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Algebraic field extensions؛ valued fields؛ polynomials in general fields | ||
| مراجع | ||
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