Geodesic
Natural homomorphisms of Witt rings of orders in algebraic number fields. II
Communications in Mathematics, Tome 14 (2006) no. 1, pp. 13-16

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We prove that there are infinitely many real quadratic number fields $K$ with the property that for infinitely many orders $\mathcal {O}$ in $K$ and for the maximal order $R$ in $K$ the natural homomorphism $\varphi :W\mathcal {O}\rightarrow WR$ of Witt rings is surjective.
Classification : 11E81, 19G12
Keywords: Witt ring; orders in number fields; bilinear forms on ideals 
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     author = {Ciema{\l}a, Marzena},
     title = {Natural homomorphisms of {Witt} rings of orders in algebraic number fields. {II}},
     journal = {Communications in Mathematics},
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     zbl = {1127.11320},
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Ciemała, Marzena. Natural homomorphisms of Witt rings of orders in algebraic number fields. II. Communications in Mathematics, Tome 14 (2006) no. 1, pp. 13-16. http://geodesic.mathdoc.fr/item/COMIM_2006__14_1_a1/