适合无限维实零点定理的序域之结构Ⅱ  

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

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2期281-288,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金

摘　　要：在本文的第二部分中，我们研究了适合无限维实零点定理的序域的结构．通过嵌入，我们证明了，一个序域适合无限维实零点定理，当且仅当它的实闭包同构于域的某个具有无限维逼近性质的子域，这里是一个无裂缝的可除序群，｛Γ｝是指数在中，系数为实数的形式幂级数域．In the second part of this paper, we investigate the structure of ordered fieldssatisfying the infinite-dimensional real Nullstellensatz. By embedding these fields intothe associated fields of power series, we prove that an ordered field satisfies the infinitedimensional real Nullstellensatz if and only if its real closure is isomorphic to somesubfield of , which has the infinite-dimensional approximation property, where is a divisible ordered group without gap, and is the field of power series withcoefficients in the field of real numbers and exponents in .

关 键 词：无限维 实零点处理 序域 形式幂级数 可除序群 

分 类 号：O153.4[理学—数学]