R0代数中素滤子的拓扑性质  

Topological Properties of Prime Filters in R_0-Algebras

作　　者：罗清君[1] 

机构地区：[1]西安财经学院数学教学部,西安710061

出　　处：《数学学报（中文版）》2008年第4期795-802,共8页Acta Mathematica Sinica：Chinese Series

摘　　要：首先讨论了R_0代数M中MP滤子、素滤子的基本性质,然后通过自然的方式在M的全体素滤子之集PF_(IL)(M)上构造拓扑,证明了PF_(IL)(M)是紧致的T_0空间.最后把PF_(IL)(M)上的拓扑限制在M的全体极大滤子之集MF_(IL)(M)上,得到MF_(IL)(M)是紧致的Hausdorff空间.In the present paper, some basic properties of MP filters and prime filters in Ro-algebra M are studied. By introducing some topological structures on the set of all prime filters and the set of all maximal filters respectively, we conclude that the set of all prime filters is a compact To topological space and the set of all maximal filters is a compact Hausdorff space.

关 键 词：R0代数 素滤子 极大滤子 

分 类 号：O141.1[理学—数学] O153[理学—基础数学]