实代数数域上的序

The orderings on a real algebraic numbers field

本文通过建立实代数数域上的序与实数之间的对应关系,对实代数数域上的序作了一个较明确的刻划,应用这些方法,最后给出了一个实代数数域是Superordered的充分必要条件。

In this paper, we discussed the ordering structure in the real algebraic extension over rational number field Q. The main result is:Let F be any formally real algebraic extension of rational number field Q, Then F is superordered if and only if there exist two orders in F at most.