A residual transcendental extension of a valuation on K to K(x1, … , xn)

Let v be a valuation of a field K, G_v its value group and k_v its residue field. Let w be an extension of v to K(x₁, … , x_n). w is called a residual transcendental extension of v if k_w/k_v is a transcendental extension. In this study a residual transcendental extension w of v to K(x₁, … , x_n) such that transdegk_w/k_v = n is defined and some considerations related with this valuation are given.