Let R be a Dedekind domain whose field of fractions is a global field. Moreover, let 𝓞 < R be an order. We examine the image of the natural homomorphism φ : W𝓞 → WR of the corresponding Witt rings. We formulate necessary and sufficient conditions for the surjectivity of φ 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/ℚ, and all quadratic function fields.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa160-4-4,
author = {Beata Rothkegel},
title = {The image of the natural homomorphism of Witt rings of orders in a global field},
journal = {Acta Arithmetica},
volume = {161},
year = {2013},
pages = {349-384},
zbl = {1294.11049},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa160-4-4}
}
Beata Rothkegel. The image of the natural homomorphism of Witt rings of orders in a global field. Acta Arithmetica, Tome 161 (2013) pp. 349-384. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa160-4-4/