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Zbl 1127.11320
Ciemała, Marzena
Natural homomorphisms of Witt rings of orders in algebraic number fields. II. (English)
[J] Acta Math. Univ. Ostrav. 14, No. 1, 13-16 (2006). ISSN 1214-8148

The author considers the natural homomorphism of Witt rings $W{\cal O} \to WR$ induced by injection of nonmaximal orders $\cal O$ of number field $K$ in the maximal order $R$ of $K$. The main theorem is as follows: \par Let ${\cal O}={\Bbb Z}[f\omega]$ be an order in real quadratic field $K$ and let $\epsilon$ be the fundamental unit in $K$. If $\epsilon^n\in{\cal O}$ for some odd natural number $n$ and if $\text{gcd}(d(K), f)=1$, then the natural homomorphism $W{\cal O} \to WR$ is surjective.
[Alfred Czogała (Katowice)]

MSC 2000:: *11E81 Algebraic theory of quadratic forms
19G12 Witt groups of rings

Citations: Zbl 1108.11036

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