The space of \(\mathbb{R}\)-places on a rational function field

DOI10.1016/J.JALGEBRA.2020.09.008zbMath1465.12008OpenAlexW3086601893MaRDI QIDQ2204848

Ron Brown, Jonathan Lee Merzel

Publication date: 16 October 2020

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2020.09.008

zbMATH Keywords

rational function fieldpath-connected spaceHarrison set\(\mathbb{R}\)-placemaximal fieldpath-connected componentspace of \(\mathbb{R}\)-places

Mathematics Subject Classification ID

Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Real algebraic and real-analytic geometry (14P99) Field arithmetic (12E30) Valued fields (12J10) General valuation theory for fields (12J20)

Cites Work

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• The structure of spaces of \(\mathbb{R}\)-places of rational function fields over real closed fields
• Inverse limits. From continua to chaos
• The reduced theory of quadratic forms
• The space of real places on \(\mathbb{R}(x; y)\)
• Extended prime spots and quadratic forms
• Maximal fields with valuations
• Embedding theorems for spaces of R-places of rational function fields and their products
• Real points and real places
• Chains of higher level orderings
• Valuations, Primes and Irreducibility in Polynomial Rings and Rational Function Fields
• Valued Fields

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