The Journal of the Indian Mathematical Society

Sudesh K. Khanduja ¹, Usha Garg ¹

Affiliations
1 Department of Mathematics, Panjab University, Chandigarh-160014, IN

Abstract

Throughout the paper K=K₀(x) denotes a simple transcendental extension of a field K₀ν₀ a Krull valuation of K₀, and ν a Prolongation of ν₀ to K. Also A₀⊆A. K₀⊆k and G₀⊆G denote respectively the valuation rings, residue fields and value groups of the Valuations ν₀ and ν. For an element ξ in A, ξ* will stand for its image in the residue field k of ν. We shall some times refer to ξ* as the ν-residue of ξ.

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Sudesh K. Khanduja ¹

Affiliations
1 Department of Mathematics, Punjab University, Chandigarh-160 014, IN

Abstract

Let F be a field of characteristic ≠ 2, k₀ = F(T), and let k be a quadratic extension of k₀. We determine explicitly (i) certain quadratic unramified extensions of k, (ii) the Geschlechterkdrper of k and (iii) the real characters of the ideal class group of the integral closure of F[T] in k.

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