About on distinguished chains

ÖZTÜRK B., ÖKE F.

Montes Taurus Journal of Pure and Applied Mathematics, cilt.6, sa.3, ss.107-110, 2024 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 6 Sayı: 3
  • Basım Tarihi: 2024
  • Dergi Adı: Montes Taurus Journal of Pure and Applied Mathematics
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.107-110
  • Anahtar Kelimeler: distinguished pairs, Lifting polynomials, transcendental extensions, Valuations
  • Trakya Üniversitesi Adresli: Evet

Özet

Let v be a valuation of a field K and a = a0, a1, …, am be a complete distinguished chain for a ∈ ¯K\K. Let va be the extension of the valuation v to the field K(a). In this study some properties provided by distinguished pairs and lifting polynomials used to define a residual algebraic free extension of v to the rational function field K(x) are obtained. The value group and residue field of the valuation va are written with the help of constants δK (ai) and minimal polynomials of the elements in the chain. In addition to the relations between value groups and residue fields of the valuations vai bi of the fields K(ai, bi) are studied by considering two chains a = a0, a1, …, am and b = b0, b1, …, bm.