R_0-代数的Stone拓扑表示定理  

Stone topological representation theorem for R_0-algebras

作　　者：周红军[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《模糊系统与数学》2010年第5期14-23,共10页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61005046);陕西省自然科学基础研究计划项目(2010JQ8020);中央高校基本科研业务费专项资金资助项目(GK200902048);陕西师范大学青年科技项目(200901010)

摘　　要：研究R0-代数中极大滤子的结构性质,通过引入有限平方交性质的概念证明了素理想定理;在全体极大滤子之集上引入了Stone拓扑,研究了Stone空间的性质;在R0-代数中引入了Boole-元的概念,证明了R0-代数的Stone拓扑表示定理,即,全体Boole-元作为Boole代数同构于该R0-代数的Stone空间中的全体既开又闭子集构成的Boole代数。Boole代数的Stone拓扑表示定理可作为该表示定理的特例而给出。In the present paper,structural properties of maximal filters in R0-algebras are studied,and an analogue of the prime ideal theorem for Boolean algebras is obtained by introducing the notion of finite square intersection property.The Stone topology is introduced on the set of all maximal filters in R0-algebras and the basic properties of the Stone space including characterizations of open/closed sets are given.Finally,the Stone topological represenation theorem for R0-algebras,which states that the subalgebra consisting of all Boolean elements in an R0-algebra is isomorphic to the Boolean algebra formed by the set of all clopen sets of the Stone space under the set-inclusion order,is established.These results show that the well-known Stone representation theorem for Boolean algebras serves as only a special case of our theorem.

关 键 词：R0-代数 有限平方交性质 素理想定理 极大滤子 Stone拓扑表示定理 

分 类 号：O141[理学—数学] O189[理学—基础数学]