TY - JOUR
ID - 2732
TI - A CLASSIFICATION OF EXTENSIONS GENERATED BY A ROOT OF AN EISENSTEIN-DUMAS POLYNOMIAL
JO - Journal of Algebraic Systems
JA - JAS
LA - en
SN - 2345-5128
AU - Nikseresht, َAzadeh
AD - Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran.
Y1 - 2024
PY - 2024
VL - 11
IS - 2
SP - 83
EP - 91
KW - Algebraic field extensions
KW - valued fields
KW - polynomials in general fields
DO - 10.22044/jas.2022.11808.1603
N2 - 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.
UR - https://jas.shahroodut.ac.ir/article_2732.html
L1 - https://jas.shahroodut.ac.ir/article_2732_348fbdd2888fbfecbecd8c5bf762901d.pdf
ER -