作 者: ;
机构地区: 肇庆学院数学与信息科学学院
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
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).