Non-archimedean directed fields K(i) with o-subfield K and i2 =-1

JOURNAL OF ALGEBRA

卷:400

Article

Rump, Wolfgang¹  Yang, Yichuan² 

[1] Univ Stuttgart, Inst Algebra & Number Theory, D-70550 Stuttgart, Germany

[2] Beihang Univ, LMIB, Dept Math, Minist Educ, Beijing 100191, Peoples R China

关键词: Directed field;    Negative square;    Segment;   

DOI  :  10.1016/j.jalgebra.2013.11.012

来源: Elsevier

【 摘 要 】

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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free