正则剩余格上滤子的若干性质  

Some properties of filters in regular residuated lattices

作　　者：吴媛[1] 

机构地区：[1]西北大学数学系,陕西西安710127

出　　处：《纺织高校基础科学学报》2010年第3期309-312,共4页Basic Sciences Journal of Textile Universities

摘　　要：在正则剩余格上给出了正蕴涵滤子的几个等价条件,引入了布尔滤子,固执滤子的概念.讨论了它们的性质及其联系,证明了在正则剩余格上布尔滤子和正蕴涵滤子是等价的.固执滤子等价于极大正蕴涵滤子与超滤,每一个固执滤子也是素滤子.Several equivalent conditions for positive implicative filter are given,and the definitions of Boolean filters,obstinate filters are introduced.The properties and relations of these filters are studied.The main results are as follow： in regular residuated lattices,Boolean filters and positive implicative filters are equivalent;obstinate filters are equivalent to maximal positive implicative filters,ultra filters;any obstinate filter is a prime filter.

关 键 词：正则剩余格 布尔滤子 正蕴涵滤子 固执滤子 

分 类 号：O141.1[理学—数学]