Minimal pairs, minimal fields and implicit constant fields

Minimal pairs of definition were introduced by Alexandru, Popescu and Zaharescu [3], [4], [5] to study residue transcendental extensions. In this paper we obtain analogous results in the value case. We introduce notion minimal fields for valuation extensions show that they share some common ramification theoretic properties. The connection between implicit constant is also investigated. Further, explore relationship pseudo-Cauchy sequences.