On Residual Transcendental Extensions of a Valuation with rankv = 2

Let v = v1 ◦ v2 be a valuation of a field K with rankv = 2. In this paper a residual transcendental extension w = w1 ◦ w2 of v to K(x) is studied where w1 and w2 are the residual extensions of v1 and v2 respectively. A characterization of lifting polynomials is given and the constants w(K,v)(c), Δ(K,v)(c), δ(K,v)(c) are defined for c, where (c, δ) ∈ K ×Gv is the minimal pair defining w.