An ordered field is a field F together with a positive cone P.
The preorderings on F are precisely the intersections of families of positive cones on F. The positive cones are the maximal preorderings.
Read more about Ordered Field: Properties of Ordered Fields, Examples of Ordered Fields, Which Fields Can Be Ordered?, Topology Induced By The Order, Harrison Topology
Famous quotes containing the words ordered and/or field:
“According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.”
—Ana Castillo (b. 1953)
“Mine was, as it were, the connecting link between wild and cultivated fields; as some states are civilized, and others half-civilized, and others savage or barbarous, so my field was, though not in a bad sense, a half-cultivated field. They were beans cheerfully returning to their wild and primitive state that I cultivated, and my hoe played the Ranz des Vaches for them.”
—Henry David Thoreau (1817–1862)