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Ordered field — In mathematics, an ordered field is a field together with a total ordering of its elements that is compatible with the field operations. Historically, the axiomatization of an ordered field was abstracted gradually from the real numbers, by… … Wikipedia
ordered field — Math. a field containing a subset of elements closed under addition and multiplication and having the property that every element in the field is either zero, in the subset, or has its additive inverse in the subset. [1940 45] * * * … Universalium
ordered field — Math. a field containing a subset of elements closed under addition and multiplication and having the property that every element in the field is either zero, in the subset, or has its additive inverse in the subset. [1940 45] … Useful english dictionary
Non-Archimedean ordered field — In mathematics, a non Archimedean ordered field is an ordered field that does not satisfy the Archimedean property. Examples are the Levi Civita field, the hyperreal numbers, the surreal numbers, the Dehn field, and the field of rational… … Wikipedia
Ordered ring — In abstract algebra, an ordered ring is a commutative ring R with a total order ≤ such that for all a, b, and c in R: if a ≤ b then a + c ≤ b + c. if 0 ≤ a and 0 ≤ b then 0 ≤ ab. Ordered rings are familiar from arithmetic. Examples include the… … Wikipedia
Field (mathematics) — This article is about fields in algebra. For fields in geometry, see Vector field. For other uses, see Field (disambiguation). In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it … Wikipedia
Glossary of field theory — Field theory is the branch of mathematics in which fields are studied. This is a glossary of some terms of the subject. (See field theory (physics) for the unrelated field theories in physics.) Definition of a field A field is a commutative ring… … Wikipedia
Field artillery in the American Civil War — M1857 Napoleon at Stones River battlefield cemetery. Field artillery in the American Civil War refers to the important artillery weapons, equipment, and practices used by the Artillery branch to support the infantry and cavalry forces in the… … Wikipedia
field trial — 1. a competition among sporting dogs under natural conditions in the field, in which the animals are judged on the basis of excellence of performance in hunting. 2. a trial of a new product or procedure to determine its efficiency or usefulness… … Universalium
Field Manual — FORCETOC Infobox Album Name = Field Manual Type = Album Artist = Chris Walla Background = #ebf5ff Recorded = Grouse Lodge, Co Westmeath, Ireland Released = flagicon|US 29 January 2008 flagicon|Australia 2 February, 2008 Recorded = Genre = Indie… … Wikipedia
