Non-Archimedean directed fields \(K(i)\) with o-subfield \(K\) and \(i^2=-1\).

DOI10.1016/j.jalgebra.2013.11.012zbMath1307.06013OpenAlexW2332631080WikidataQ112881561 ScholiaQ112881561MaRDI QIDQ405801

Wolfgang Rump, Yi Chuan Yang

Publication date: 8 September 2014

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2013.11.012

zbMATH Keywords

positive conesnon-Archimedean fieldsdirected fieldsdirected partial orderslinearly ordered fieldsmultiplicative segmentspartially ordered algebras

Mathematics Subject Classification ID

Ordered rings, algebras, modules (06F25) Ordered topological linear spaces, vector lattices (46A40) Ordered fields (12J15)

Related Items (6)

Directed partial orders over non-Archimedean \(o\)-fields ⋮ Some questions on partially ordered rings – a survey ⋮ Note on classification of two-dimensional associative lattice-ordered real algebras ⋮ Directed partial orders on complex numbers and quaternions over non-Archimedean linearly ordered fields ⋮ Hereditary ℓ-ideals of matrix rings over ℓ-rings ⋮ Directed partial orders on the field of generalized complex numbers with \(1\not >0\)

Cites Work

• Fields with directed partial orders
• Lattice-ordered fields
• On the existence of directed rings and algebras with negative squares
• Note on Lattice-ordered Rings with Positive Squares
• Note on ordered groups and rings
• On Elements with Negative Squares
• A Lattice-Ordered Skew Field Is Totally Ordered If Squares Are Positive
• LINEAR ORDERS ON RINGS
• On Ordered Domains of Integrity
• On Ordered Skew Fields
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