Non-archimedean directed fields K(i) with o-subfield K and i(2) =-1

作者：Rump Wolfgang; Yang Yichuan^*

来源：Journal of Algebra, 2014, 400: 1-7.

DOI：10.1016/j.jalgebra.2013.11.012

• Directed field
• Negative square
• Segment

Let K be a linearly ordered field, and let i be a root of the equation x(2) + 1 = 0. If K is archimedean, it is known that K(i) cannot be a 2 dimensional directed algebra over K. For non-archimedean K, however, Yang (2006) [17] proved the existence of directed fields K(i) that are 2 dimensional directed algebras over K. In this paper, we characterize directed fields of the form K(i) that extend the order of K.

• 出版日期2014-2-15
• 单位北京航空航天大学