Orderings, real places, and valuations on noncommutative integral domains

DOI10.1006/jabr.1998.7630zbMath0934.16041OpenAlexW2051432937MaRDI QIDQ1284106

Murray A. Marshall, Yu-Fei Zhang

Publication date: 2 February 2000

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

Full work available at URL: https://doi.org/10.1006/jabr.1998.7630

zbMATH Keywords

orderingsintegral domainsfansquantum planesreal placesBröcker's trivialization theoremorder compatible real placesreal spectra of noncommutative rings

Mathematics Subject Classification ID

Rings arising from noncommutative algebraic geometry (16S38) Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Semialgebraic sets and related spaces (14P10) Topological and ordered rings and modules (16W80) Integral domains (associative rings and algebras) (16U10)

Related Items (10)

The Noncommutative Graded Positivstellensatz ⋮ Real spectra of quantum groups ⋮ Orderings of higher level on noetherian rings ⋮ \(n\)-real valuations and the higher level version of the Krull-Baer theorem. ⋮ Valuations and orderings on the real Weyl algebra ⋮ The real spectrum of a noncommutative ring and the Artin-Lang homomorphism theorem ⋮ Embedding ordered valued domains into division rings ⋮ Complete precones on noncommutative integral domains ⋮ 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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• The reduced theory of quadratic forms
• Witt rings and orderings of skew fields
• Characterization of fans and hereditarily pythagorean fields
• The real spectrum of a noncommutative ring
• Spaces of orderings and abstract real spectra
• Real places and ordered fields
• Quadratic forms over arbitrary fields

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