On a real places of a field and their holomorphy ring

DOI10.1080/00927878208822775zbMath0509.14026OpenAlexW1966588727MaRDI QIDQ4748273

Heinz-Werner Schülting

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1080/00927878208822775

zbMATH Keywords

class groupNullstellensatzreduced Witt ringreal holomorphy ringspace of orderingsreal valuation rings

Mathematics Subject Classification ID

Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Valuations and their generalizations for commutative rings (13A18) Relevant commutative algebra (14A05) Ordered fields (12J15) General valuation theory for fields (12J20) Real-analytic manifolds, real-analytic spaces (32C05) Forms over real fields (11E10) Real algebraic and real-analytic geometry (14Pxx)

Related Items (15)

Prime divisors on real varieties and valuation theory ⋮ Application signature et anneaux archimédiens ⋮ Sheaves of abelian \(l\)-groups ⋮ Chain signatures and higher level Witt rings ⋮ COMPLETELY REAL HULLS OF PARTIALLY ORDERED RINGS ⋮ Density of composite places in function fields and applications to real holomorphy rings ⋮ Topological spaces as spaces of \(\mathbb R\)-places ⋮ Real holomorphy rings and the complete real spectrum ⋮ SV-rings and SV-porings ⋮ Convex subrings of partially ordered rings ⋮ Number of connected components of a real variety and \(\mathbb{R}\)-places ⋮ Sums of mixed powers in fields and orderings of prescribed level ⋮ On relative real holomorphy rings ⋮ Metrizability of Spaces of ℝ-places of Function Fields of Transcendence Degree 1 Over Real Closed Fields ⋮ The holomorphy rings of planar ternary rings with rational prime field

Cites Work

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• Die Modelle des Hilbertschen Axiomensystems der absoluten Geometrie
• The Nullstellensatz over \(\mathfrak p\)-adically closed fields
• Lotschnittebenen mit halbierbarem rechtem Winkel
• The prime ideals of Witt rings
• Real places and ordered fields
• The theory of real places
• Partial orders on a field and valuation rings
• Über die erzeugendenanzahl invertierbarer ideale in prüferringen
• La topologie du spectre réel
• Real points and real places
• The weak local global principle in algebraic k-theory

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