Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Acta Arithmetica / All issues

Abstract

Let $R$ be a Dedekind domain whose field of fractions is a global field. Moreover, let $\mathcal O < R$ be an order. We examine the image of the natural homomorphism $\varphi \colon W\mathcal {O}\to WR$ of the corresponding Witt rings. We formulate necessary and sufficient conditions for the surjectivity of $\varphi$ in the case of all nonreal quadratic number fields, all real quadratic number fields $K$ such that $-1$ is a norm in the extension $K/\mathbb Q$, and all quadratic function fields.