A characterization of rings in which each partial order is contained in a total order

DOI10.1090/S0002-9939-97-03933-6zbMath0880.06009OpenAlexW1513631778MaRDI QIDQ4372354

Stuart A. Steinberg

Publication date: 11 December 1997

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-97-03933-6

zbMATH Keywords

ordered rings\(O^*\)-rings\(O^*\)-fieldextension of partial order to total orderquadratic extension of the rationalssubrings of algebras over the rationals

Mathematics Subject Classification ID

Ordered rings, algebras, modules (06F25)

Related Items (8)

The number fields that are \(O^*\)-fields ⋮ Extending orders on rings with idempotents and d-elements ⋮ Division closed lattice-ordered rings ⋮ Some questions on partially ordered rings – a survey ⋮ Galois extensions and \(O^*\)-fields ⋮ Commutative L*-rings II ⋮ Division closed ℓ-rings and power positive L^∗-rings ⋮ Division closed lattice-ordered rings and commutative L*-rings

Cites Work

• Lattice ordered rings and function rings
• Groupes et anneaux reticules
• If a polynomial identity guarantees that every partial order on a ring can be extended, then this identity is true only for a zero-ring
• Quotient Rings of a Class of Lattice-Ordered-Rings
• On ordered algebras
• Unnamed Item
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• Unnamed Item

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