关于KRULL型整环的性质的描述  

Characterizations on Krull Type Domain

作　　者：杨杰[1] 王芳贵[1] 

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2005年第3期287-290,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金项目(10271052);四川省应用基础研究基金;四川省重点学科基金资助项目

摘　　要：证明了有单位元的整环R是Krull型整环,当且仅当R[X]是Krull型整环,当且仅当R[X]Nv是Krull型整环.另外,证明了R是赋值环当且仅当R是局部的Krull型整环,且R是TL整环,Spec(R)是全序.同时,还证明了R是Krull整环当且仅当R既是Krull型整环又是H整环,且dim(R)=1.最后,证明了R是Krull型整环,那么R的每个t linked扩环是Krull型整环,R在商域K的有限代数扩域L中的w 整闭包RwL有PIT当且仅当w dim(R)=1.In this paper, we prove that R is a Krull type domain if and only if R is a Krull type domain, if and only if R_(N_v) is also a Krull type domain. Moreover, we prove that R is a valuation domain if and only if R is a quasi-local Krull type domain and R is a TL domain and Spec(R) is totally ordered. We also prove that R is a Krull domain if and only if R is a Krull type domain and R is an H domain and dim(R)=1. Finally, we prove that each t-linked overring of a Krull type domain is a Krull type domain, that the w-integral closure R^w_L of a Krull type domain has PIT property if and only if w-dim(R)=1.

关 键 词：Krull整环 Krull型整环 t-linked扩环 w-整环 

分 类 号：O154[理学—数学]