Some constants and tame extensions according to a valuation of a field with rank v = 2

ÖZTÜRK B., ÖKE F.

Proceedings of the Jangjeon Mathematical Society, cilt.15, sa.4, ss.477-482, 2012 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 4
  • Basım Tarihi: 2012
  • Dergi Adı: Proceedings of the Jangjeon Mathematical Society
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.477-482
  • Anahtar Kelimeler: Krasner's constant, Tame extensions, Valued fields
  • Trakya Üniversitesi Adresli: Evet

Özet

Let v = v1 ° v2 be a valuation of a field K with rankv = 2 and v̄ be the extension of v to the algebraic closure K̄ of K. Let (L, z)/(K, v) be a finite extension of valued fields where z = z 1 ° z2 be the extension of v to field L. In this paper it is shown that, if (L, z)/(K, v) be a tame extension then finite extensions of valued fields (L, z1)/(K, v1) and (kz1, z2)/(kv1, v2) are tame extensions. Also Krasner's constant of an element α ∈ K̄\K is obtained as w (k, v) (α) = (w(K, v1) (α), w(kv1, v2) (α*)) and the other constants of α are obtained as Δ(K, v) (α) = (Δ(K, V1) (α), Δ(kv1, v2) (α*)) and δ(K, v) (α) = (δ(K,v1) (α), δ(kv1 V1)(α*)).