Let v(0) be a valuation of a field K-0 with value group G(0). Let K be a function field of a conic over K-0, and let v be an extension of v(0) to K with value group G such that G/G(0) is not a torsion group. Suppose that either (K-0, v(0)) is henselian or v(0) is of rank 1, the algebraic closure of K-0 in K is a purely inseparable extension of K-0, and G(0) is a cofinal subset of G. In this paper, it is proved that there exists an explicitly constructible element 1 in K, with v(t) non-torsion module G(0) such that the valuation of K-0(t), obtained by restricting v, has a unique extension to K. This generalizes the result proved by Khanduja in the particular case, when K is a simple transcendental extension of K-0 (compare [4]). The above result is an analogue of a result of Polzin proved for residually transcendental extensions [8]. [References: 9]
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