| Autor: |
Faris, Mohamed, El Fadil, Lhoussain |
| Zdroj: |
Tatra Mountains Mathematical Publications; February 2023, Vol. 83 Issue: 1 p87-102, 16p |
| Abstrakt: |
Let | | be a discrete non-archimedean absolute value of a field Kwith valuation ring 𝒪, maximal ideal 𝓜and residue field 𝔽 = 𝒪/𝓜. Let Lbe a simple finite extension of Kgenerated by a root αof a monic irreducible polynomial F∈ O[x]. Assume that F¯=ϕ¯l$\overline F = \overline \varphi ^l$in 𝔽[x] for some monic polynomial φ∈ O[x] whose reduction modulo 𝓜is irreducible, the φ-Newton polygon Nφ¯(F)$N\overline \phi \left( F \right)$has a single side of negative slope λ, and the residual polynomial Rλ(F)(y) has no multiple factors in 𝔽φ[y]. In this paper, we describe all absolute values of Lextending | |. The problem is classical but our approach uses new ideas. Some useful remarks and computational examples are given to highlight some improvements due to our results. |
| Databáze: |
Supplemental Index |
| Externí odkaz: |
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