A characterization of algebraic elements of prime degree by using valuation basis

Author
Azadeh Nikseresht
Department of Mathematics, Faculty of Basic Sciences, Ayatollah Boroujerdi University, Boroujerd, Iran.
Abstract
Algebraic elements of prime degree hold a prominent position in the study of the extensions in valuation theory. Moreover, distinguished pairs and saturated (complete) distinguished chains are useful tools in exploring the properties of algebraic extensions and polynomials over valued fields. In this paper for every algebraic element of prime degree over a henselian valued field, we present a classification of distinguished pairs and saturated distinguished chains by using the concept of valuation basis.
Keywords
valued fields
field extensions
algebraic elements of prime degree
distinguished pair
saturated distinguished chain
valuation basis
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