R_0-代数(NM-代数)的布尔MP滤子与布尔MP理想  

Boolean MP-filters and Boolean MP-ideals in R0-algebras (NM-algebras)

作　　者：张小红[1] 薛占熬[2] 马盈仓[2] 

机构地区：[1]宁波大学理学院,宁波315211 [2]西北工业大学计算机学院,西安710072

出　　处：《工程数学学报》2005年第2期287-294,共8页Chinese Journal of Engineering Mathematics

基　　金：宁波市青年基金(2004AB20017)宁波大学科研基金

摘　　要：在Ro-代数中引入布尔MP滤子与布尔MP理想的概念,给出其若干充要条件,研究了它们与素滤子、极大MP滤子的关系。通过反例指出了关于超MP滤子的一个错误结论,给出超MP滤子的一个充分必要条件。在此基础上研究了Ro-代数的结构,用布尔MP滤子与布尔MP理想刻画了二部Ro-代数、强二部Ro-代数的特征。The notions of Boolean MP-filter and Boolean MP-ideal in Ro-algebra (NM-algebra) are introduced and some sufficient and necessary conditions for them are proved. The relations between prime filter and maximum MP-filter are studied, an equivalent condition for a MP-filter to be ultra MP-filter is obtained, and a mistake result about ultra MP-filter is pointed out. Using these results the structures of Ro-algebra are studied, characterizations of Bipartite Ro-algebra and ultra Bipartite Ro-algebra are described by Boolean MP-filter and Boolean MP-ideal.

关 键 词：FUZZY逻辑 R0-代数 布尔MP滤子 布尔MP理想 超MP滤了 二部R0-代数 

分 类 号：O141.1[理学—数学] O159[理学—基础数学]