Volume 10, Issue 3 (11-2024)
mmr 2024, 10(3): 136-150 |
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Nikseresht A. A characterization of algebraic elements of prime degree by using valuation basis. mmr 2024; 10 (3) :136-150
URL: http://mmr.khu.ac.ir/article-1-3197-en.html
URL: http://mmr.khu.ac.ir/article-1-3197-en.html
Department of Mathematics, Faculty of Basic Sciences, Ayatollah Boroujerdi University, Boroujerd, Iran. , azade.nikseresht@gmail.com
Abstract: (116 Views)
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.
Type of Study: Original Manuscript |
Subject:
alg
Received: 2021/05/10 | Revised: 2024/11/9 | Accepted: 2024/09/3 | Published: 2024/11/6 | ePublished: 2024/11/6
Received: 2021/05/10 | Revised: 2024/11/9 | Accepted: 2024/09/3 | Published: 2024/11/6 | ePublished: 2024/11/6
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