态BL-代数上的微分  

On Derivations of State BL-algebras

作　　者：王伟 辛小龙[1] 王军涛[1] 

机构地区：[1]西北大学数学学院,陕西西安710127

出　　处：《模糊系统与数学》2016年第6期52-59,共8页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11571281)

摘　　要：在态BL-代数(A,σ)上引入(⊙,∨)-微分,研究了态BL-代数(A,σ)上(⊙,∨)-微分的性质。定义并研究了态BL-代数(A,σ)上正则微分和强微分,给出了正则强微分成为保序微分的等价条件。给出态BL-代数上的主微分的概念,讨论了全体主微分的代数结构,并利用Galois联结给出主微分的微分伴随。最后在态BL-代数(A,σ)上引入了不动点集A_(dσ),得到若d为正则保序的强微分时,A_(dσ)为A的格理想。我们的研究思路旨在将BL-代数上的态结构与微分结构紧密融合,以此来研究BL-代数的结构。The notion of （⊙, V ）-derivations on state BL-algebras （A, σ） is introduced and some properties of them are discussed. The regular derivations and strong derivations are given and investigated. Some equivalent characterizations about the isotone derivation in state morphism BL-algebras be provided. Moreover, the adjoint of a principal derivation is obtained by Galois connection. In the last, the fixed set of a derivation in state BL-algebras （A ,σ） are introduced and it is obtained that Adσ is a lattice ideal of A, when derivation d is a regular,isotone and strong. Our research is aimed to study the structures of BL-algebras through combining state operators and derivations in BL-algebras.

关 键 词：态BL-代数 微分态BL-代数 Galois联结 不动点集 

分 类 号：O143[理学—数学]