Abstract

In this paper studying on value groups and residue fields of valued rational function fields and valued function fields of conics is purposed. Let F be a function field over K; v be a valuation on K ; w be an extension of v to F; kw, ky and Gw, Gy be residue fields and value groups of w and v respectively. If F is rational function field over K then either k/kv is an algebraic extension or kw is a simple transcendental extension of any finite extension of kv. If F is a function field of conic over K and chark ≠ 2 then either kw/ky is an algebraic extension or kw is a regular function field of conics over any finite extension of ky. In the both case either Gw/Gy is a torsion group or there exists a subgroup G₁ of Gw such that G/G is a torsion group and Gw is the direct sum of G₁ and an infinite cyclic group.