*-Orderings on a ring with involution

DOI10.1080/00927870008826887zbMath0955.16029OpenAlexW2058330191MaRDI QIDQ4947072

Murray A. Marshall

Publication date: 22 June 2000

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

Full work available at URL: https://doi.org/10.1080/00927870008826887

zbMATH Keywords

valuationsrings with involutionssymmetric elementsJordan orderingsskewfieldsBaer orderingsspaces of signs

Mathematics Subject Classification ID

Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) General theory of (C^*)-algebras (46L05) Topological and ordered rings and modules (16W80) Skew fields, division rings (12E15) Ordered rings (13J25) General valuation theory for fields (12J20)

Related Items (17)

Real spectra of quantum groups ⋮ Valuation theory of higher level *-signatures ⋮ Free skew fields have many *-orderings. ⋮ Orderings and \(*\)-orderings on cocommutative Hopf algebras ⋮ The Joly-Becker theorem for \(*\)-orderings ⋮ Maximal quadratic modules on \(*\)-rings. ⋮ Residually *-Abelian Valuation with Residue Characteristic Not 2 ⋮ Ordered \(*\)-rings ⋮ On \(*\)-orderable groups. ⋮ A strict Positivstellensatz for the Weyl algebra ⋮ \(*\)-orderable semigroups. ⋮ A strict Positivstellensatz for enveloping algebras ⋮ Embedding \(*\)-ordered domains into skew fields. ⋮ Local-global properties of positive primitive formulas in the theory of spaces of orderings ⋮ Residually *-Abelian Valuation ⋮ On 𝑞-normal operators and the quantum complex plane ⋮ *-orderings and *-valuations on algebras of finite Gelfand-Kirillov dimension.

Cites Work

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• Orderings and valuations on *-fields
• An introduction to real algebra
• Rings with involution as partially ordered Abelian groups
• Witt groups of Hermitian forms over \(\ast\)-fields
• The real spectrum of a noncommutative ring

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