Ordered Field

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:

    The case of Andrews is really a very bad one, as appears by the record already before me. Yet before receiving this I had ordered his punishment commuted to imprisonment ... and had so telegraphed. I did this, not on any merit in the case, but because I am trying to evade the butchering business lately.
    Abraham Lincoln (1809–1865)

    Mothers seem to be in subtle competition with teachers. There is always an underlying fear that teachers will do a better job than they have done with their child.... But mostly mothers feel that their areas of competence are very much similar to those of the teacher. In fact they feel they know their child better than anyone else and that the teacher doesn’t possess any special field of authority or expertise.
    Sara Lawrence Lightfoot (20th century)