Real reduced multirings and multifields

DOI10.1016/j.jpaa.2005.07.011zbMath1089.14009OpenAlexW2158874717MaRDI QIDQ819806

Murray A. Marshall

Publication date: 29 March 2006

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2005.07.011

Mathematics Subject Classification ID

Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Semialgebraic sets and related spaces (14P10) Real algebra (13J30)

Related Items (26)

An equivalence between two approaches to limits of local fields ⋮ Hyperstructures of affine algebraic group schemes ⋮ Witt rings of quadratically presentable fields ⋮ K-theories and Free Inductive Graded Rings in Abstract Quadratic Forms Theories ⋮ Algebraic geometry over hyperrings ⋮ Calculus of meet plus hyperalgebra (tropical semihyperrings) ⋮ On profinite spaces of orderings ⋮ Semiring systems arising from hyperrings ⋮ On the relation between hyperrings and fuzzy rings ⋮ Witt equivalence of function fields over global fields ⋮ On basic concepts of tropical geometry ⋮ Matroids over partial hyperstructures ⋮ Real holomorphy rings and the complete real spectrum ⋮ Geometry of hyperfields ⋮ Witt equivalence of fields: A survey with a special emphasis on applications of hyperfields ⋮ On the structure of hyperfields obtained as quotients of fields ⋮ Orderings and signatures of higher level on multirings and hyperfields ⋮ Classification of doubly distributive skew hyperfields and stringent hypergroups ⋮ Quotients of index two and general quotients in a space of orderings ⋮ Unnamed Item ⋮ A survey of selected categorical properties of algebras with multivalued addition ⋮ Orderings and valuations in hyperfields ⋮ Functorial relationships between multirings and the various abstract theories of quadratic forms ⋮ Fans in the theory of real semigroups ⋮ Graphs derived from multirings ⋮ Height of prime hyperideals in Krasner hyperrings

Cites Work

• Spaces of orderings and abstract real spectra
• Special groups: Boolean-theoretic methods in the theory of quadratic forms
• Open questions in the theory of spaces of orderings
• Prime Ideal Structure in Commutative Rings
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