适合无限维实零点定理的序域之结构Ⅰ  

On Structure of Ordered Fields Satisfying the Infinite-dimensional Real Nullstellensatz I

作　　者：曾广兴[1] 

机构地区：[1]南昌大学数学与系统科学系,南昌330047

出　　处：《数学学报（中文版）》1999年第1期125-132,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金

摘　　要：本文的目的是建立适合无限维实零点定理的序域的结构定理．作为预备工作，文章的第一部分研究一类无秩为d的裂缝的序群，这里d是无限基数．藉助于Hahn嵌入定理，本文给出了无秩为d的裂缝的序群的结构．The purpose of this paper is to establish a theorem on structure of ordered fields satisfying the infinite-dimensional real Nullstellensatz. For the preliminaries, in the first part of this paper, a class of ordered groups, which have no gap of rank d for an infinite cardinal number d, is investigated. With the aid of Hahn Embeding Theorem,we give the structure of ordered groups without gap of rank d for an infinite cardinal numberd.

关 键 词：无限维 实零点定理 序域 序群 裂缝 

分 类 号：O153.4[理学—数学]