Definition 42.68.31. Let A be a Noetherian local domain of dimension 1 with residue field \kappa . Let K be the fraction field of A. We define the tame symbol of A to be the map
K^* \times K^* \longrightarrow \kappa ^*, \quad (x, y) \longmapsto d_ A(x, y)
where d_ A(x, y) is extended to K^* \times K^* by the multiplicativity of Lemma 42.68.30.
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