交换环上高层序与赋值对的相容性  

Compatibility of an ordering of higher level with a valuation pair for a commutative ring

作　　者：邹群[1] 

机构地区：[1]南昌航空工业学院信息与计算科学系,江西南昌330034

出　　处：《南昌航空工业学院学报》2005年第1期13-16,共4页Journal of Nanchang Institute of Aeronautical Technology（Natural Science Edition）

摘　　要：本文的主要目的是把域上高层序与赋值对的相容性推广到含单位元的交换环上来。本文提出了交换环上高层序与赋值对相容的概念,由此得到高层序与赋值对相容的四个等价条件。本文的关键是藉助于赋值环的凸性来刻划高层序与赋值对的相容性。本文的方法是通过取序的特殊化以及整环的商域,使环的情形下的问题转化到域的情形来解决。The main aim of this paper is to extend the compatibility of an ordering of higher level with a valuation pair on a field to a commutative ring with unit. We introduce the concept of compatibility of an ordering of higher level with a valuation pair for a commutative ring with u-nit. Then we give four equivalent conditions for an ordering of higher level to be compatible with a valuation pair. It is a key in this paper to characterize the compatibility of an ordering of higher level with a valuation pair by means of the convexity of the valuation ring. The technique of this paper is to convert the problems in the case of rings into that of fields by taking specializations of orderings and the quotient fields of domains.

关 键 词：相容性 交换环 层序 等价条件 问题转化 单位元 赋值环 特殊化 刻划 凸性 商域 整环 

分 类 号：O153.3[理学—数学] TQ334.9[理学—基础数学]