Fuzzy格中理想的最小同余扩张  

The smallest congruence extensions of ideals in Fuzzy lattices

作　　者：朱怡权[1] 

机构地区：[1]肇庆学院数学系,广东肇庆526061

出　　处：《华中师范大学学报（自然科学版）》2004年第1期21-23,共3页Journal of Central China Normal University：Natural Sciences

基　　金：广东省自然科学基金资助项目(021073).

摘　　要：刻画了Fuzzy格中理想的最小同余扩张,设I为Fuzzy格F的任一理想,令Tc(I)={x∈F| d∈I,使得x∧d′≤d∧d′},则Tc(I)是F中包含I的最小同余理想.证明了正规Fuzzy格(或Kleene代数)F中,理想E={x∧x′|x∈F}的最小同余扩张是一个W-理想,即存在唯一的同余关系以它为核.In this paper,we describe the characterization of the smallest congruence extensions of ideals in a Fuzzy lattice: suppose F is Fuzzy lattice, I is an ideal of F, let( T_c(I))={x∈F|d∈I, such that x∧d′≤d∧d′},then T_c(I) is the smallest congruence ideal containing I. Moreover, it is proved that in a normal Fuzzy lattice F(or Kleene algebra F) the smallest congruence extension of the ideal E={x∧x′|x∈F} is a W-ideal, that is to say, there is the unique congruence relation with kernel T_c(E).

关 键 词：FUZZY格 同余关系 同余理想 W-理想 同余扩张 

分 类 号：O153[理学—数学]