Orderings and valuations on *-fields

DOI10.1216/RMJ-1989-19-3-629zbMath0702.16007OpenAlexW2110425236MaRDI QIDQ914799

Thomas C. Craven

Publication date: 1989

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmj-1989-19-3-629

zbMATH Keywords

automorphisminvolutionskew fieldvaluationcommutatorvalue groupresidue class fieldtotal orderingBaer orderingJordan orderingslifting orderingsproduct of smooth elementssmooth semi-sectionsmooth valuationsymmetric element

Mathematics Subject Classification ID

Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Infinite-dimensional and general division rings (16K40) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Ordered rings, algebras, modules (06F25) Ordered fields (12J15) Valued fields (12J10)

Related Items (13)

Valuation theory of higher level *-signatures ⋮ Free skew fields have many *-orderings. ⋮ Indecomposable division algebras with a baer ordering ⋮ Places on ∗- fields and the real holomorphy ring ⋮ Characterization of fans in *-fields ⋮ Pythagorean \(*\)-fields ⋮ Witt groups of Hermitian forms over \(\ast\)-fields ⋮ The Joly-Becker theorem for \(*\)-orderings ⋮ Ordered \(*\)-rings ⋮ ^*-Orderings on a ring with involution ⋮ Embedding \(*\)-ordered domains into skew fields. ⋮ Hermitian forms over ordered *-fields ⋮ *-orderings and *-valuations on algebras of finite Gelfand-Kirillov dimension.

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