幂等剩余格  

Idempotent Residuated Lattices and psG-filters

作　　者：任兰[1] 张小红[2] 

机构地区：[1]宁波大学理学院,浙江宁波315211 [2]上海海事大学文理学院,上海201306

出　　处：《模糊系统与数学》2011年第3期21-29,共9页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(60775038)

摘　　要：研究一种特殊的剩余格——幂等剩余格,证明满足幂等性的一般剩余格必是可换剩余格,即不存在非可换的幂等剩余格。讨论幂等剩余格的基本性质以及与各类特殊剩余格之间的关系。在一般剩余格中引入psG-滤子的概念,给出其一组等价条件,并借助psG-滤子刻画幂等剩余格的特征。This paper is concerned with a special residuated lattice — idempotent residuated lattice,and it is proved that if a general residuated lattice is idempotent then it is commutative residuated lattice,in other words,non-commutative residuated lattice does not exist.The basic properties of idempotent residuated lattices are studied and the relation of several special residuated lattices are discussed.Moreover,in general residuated lattice the concept of psG-filter is introduced and some equivalence conditions are given.Based on these results,idempotent residuated lattice is characterized by psG-filters.

关 键 词：剩余格 可换剩余格 幂等剩余格 幂等子集 psG-滤子 

分 类 号：O153[理学—数学] O141[理学—基础数学]