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Natural homomorphisms of Witt rings of orders in algebraic number fields. II. (English) Zbl 1127.11320
The author considers the natural homomorphism of Witt rings \(W{\mathcal O} \to WR\) induced by injection of nonmaximal orders \(\mathcal O\) of number field \(K\) in the maximal order \(R\) of \(K\). The main theorem is as follows:

Let \({\mathcal O}={\mathbb Z}[f\omega]\) be an order in real quadratic field \(K\) and let \(\epsilon\) be the fundamental unit in \(K\). If \(\epsilon^n\in{\mathcal O}\) for some odd natural number \(n\) and if \(\text{gcd}(d(K), f)=1\), then the natural homomorphism \(W{\mathcal O} \to WR\) is surjective.
11E81 Algebraic theory of quadratic forms; Witt groups and rings
19G12 Witt groups of rings
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