A Remark on Quadratic Spaces over Noncommutative Semilocal Rings.
Bernhard Keller (1988)
Mathematische Zeitschrift
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Displaying similar documents to “About the Witt rings of function fields of algebroid quadratic quasihomogeneous surfaces.”
A Remark on Quadratic Spaces over Noncommutative Semilocal Rings.
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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.
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Richard Elman, Jón Kr. Arason, Bill Jacob (1985)
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H.K. Farahat, L. Mirsky (1958)
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Faithfully quadratic rings - a summary of results
M. Dickmann, F. Miraglia (2016)
Banach Center Publications
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This is a summary of some of the main results in the monograph Faithfully Ordered Rings (Mem. Amer. Math. Soc. 2015), presented by the first author at the ALANT conference, Będlewo, Poland, June 8-13, 2014. The notions involved and the results are stated in detail, the techniques employed briefly outlined, but proofs are omitted. We focus on those aspects of the cited monograph concerning (diagonal) quadratic forms over preordered rings.
On a class of right alternative rings.
Erwin Kleinfeld (1965)
Mathematische Zeitschrift
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On an isotropy criterion for quadratic forms over function fields of curves over non-dyadic complete discrete valuation rings
David Grimm (2016)
Banach Center Publications
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Harbater, Hartmann and Krashen obtained in 2015 a criterion for the existence of rational points on projective (or principal) homogeneous varieties for rational connected algebraic groups defined over function fields of normal curves over a complete discrete valuation ring in terms of completions of local rings at special points. This was obtained by a reduction via Artin approximation to a related patching problem solved by the same authors in 2009. In the special case of projective...