MTL-代数的演绎系统和余零化子及其相互关系  

The Deductive System and Co-annihilator of MTL-algebras and the Relation between Them

作　　者：王娜[1] 吴洪博[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《模糊系统与数学》2014年第1期9-14,共6页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11171196)

摘　　要：首先,在MTL-代数中给出了演绎系统的定义;其次,提出了MTL-代数余零化子的概念,并研究了它们的一些基本性质;最后,讨论了MTL-代数中余零化子与演绎系统的关系,证明了MTL-代数的演绎系统A的余零化子A⊥是素的演绎系统的充要条件:A是线性的且A≠{1}。Firstly, the definition of deductive system is given and its properties are investigated on the MTL-algebras Secondly, the concept of co-annihilator is introduced and its behavior is discussed in the MTL-algebras; Finally, the relation between co-annihilator and deductive system is researched in the MTL-algebras, and it is proved that in the MTL-algebras the co-annihilator A^⊥ of a deductive system A is a prime deductive system if and only if A is linear and A=/= {1}.

关 键 词：MTL一代数 余零化子 演绎系统 剩余格 关系 

分 类 号：O141[理学—数学]