Witt rings and orderings of skew fields

DOI10.1016/0021-8693(82)90278-2zbMath0493.10026OpenAlexW1998557894MaRDI QIDQ1168353

Thomas C. Craven

Publication date: 1982

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(82)90278-2

zbMATH Keywords

Witt ringskew fieldsspace of orderingsArtin- Schreier results on ordered fields for higher-level orderingsmethods of algebraic theory of quadratic formsreduced Witt ring of an ordered skew fieldStufeWitt- Grothendieck rings

Mathematics Subject Classification ID

Topological and ordered rings and modules (16W80) Skew fields, division rings (12E15) Forms over real fields (11E10)

Related Items (32)

Witt rings of quaternion algebras ⋮ The Noncommutative Graded Positivstellensatz ⋮ Orderings of higher level on noetherian rings ⋮ \(n\)-real valuations and the higher level version of the Krull-Baer theorem. ⋮ On Witt Rings of Quaternion Algebras over 1-Hilbert Fields ⋮ Higher level orders on noncommutative rings ⋮ A simple system of axioms for spaces of signatures ⋮ The real spectrum of a noncommutative ring ⋮ Spaces of orderings and Witt rings of planar ternary rings ⋮ Valuations and orderings on the real Weyl algebra ⋮ On the topological space of all orderings of a skew field ⋮ An abstract approach to higher level forms and rigidity ⋮ Witt rings of weakly orderable double loops and nearfields ⋮ Characterization of fans in *-fields ⋮ Wittringe höherer Stufe ⋮ Structure theorems for AP rings ⋮ Central Extensions of n-Ordered Division Rings ⋮ Witt groups of Hermitian forms over \(\ast\)-fields ⋮ HIGHER PRODUCT LEVELS OF NONCOMMUTATIVE RINGS ⋮ The Joly-Becker theorem for \(*\)-orderings ⋮ Quadratic Forms ⋮ Complete precones on noncommutative integral domains ⋮ Higher level reduced Witt rings of skew fields ⋮ Witt rings of division algebras over global fields ⋮ Holomorphy rings and higher level orders on skew fields ⋮ A Variant of Higher Product Levels of Integral Domains and *-Domains ⋮ Orderings, real places, and valuations on noncommutative integral domains ⋮ Local-global properties of positive primitive formulas in the theory of spaces of orderings ⋮ Lokal-global Prinzipien für Anordnungen bewerteter Schiefkörper ⋮ Orderings on semirings ⋮ Central extensions of ordered skew fields ⋮ *-orderings and *-valuations on algebras of finite Gelfand-Kirillov dimension.

Cites Work

• Orderings of higher level and semilocal rings
• Succinct and representational Witt rings
• The topological space of orderings of a rational function field
• Characterizing reduced Witt rings of fields
• Characterizing reduced Witt rings. II
• On the description of the reduced Witt ring
• Signatures on semilocal rings
• The Witt Ring of a Space of Ordering
• Spaces of Orderings IV
• Summen n-ter Potenzen in Körpern.
• Classification of Finite Spaces of Orderings
• Structure of Witt Rings and Quotients of Abelian Group Rings
• On Ordered Division Rings
• On Ordered Skew Fields
• On Ordered Division Rings
• On ordered algebras
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