ordered field

noun

A field which has an order relation satisfying these properties: trichotomy, transitivity, preservation of an inequality when the same element is added to both sides, and preservation of an inequality when the same strictly positive element is multiplied to both sides.

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Meanings

nounordered field (plural ordered fields)

plural ordered fields

  1. algebraA field which has an order relation satisfying these properties: trichotomy, transitivity, preservation of an inequality when the same element is added to both sides, and preservation of an inequality when the same strictly positive element is multiplied to both sides.

Translations

Polish ciało uporządkowane
  • ciało uporządkowanefield satisfying the properties of trichotomy, transitivity and preservation of an inequality when the same element is added to both sides
Portuguese corpo ordenado
  • corpo ordenadofield satisfying the properties of trichotomy, transitivity and preservation of an inequality when the same element is added to both sides
Romanian corp ordonat
  • corp ordonatfield satisfying the properties of trichotomy, transitivity and preservation of an inequality when the same element is added to both sides
Cite this entry
APA

ordered field. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/ordered%20field

MLA

“ordered field.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/ordered%20field. Accessed November 3, 2026.

Chicago

WatkinsX Dictionary, s.v. “ordered field,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/ordered%20field.

Source: ordered field on Wiktionary, CC BY-SA 4.0.