基于剩余格理论的P-有界分配格的理想集代数  

Ideal Sets Algebra of P-bounded Distributive Lattice Based on Theory of Residual Lattices

作　　者：李小杰[1,2] 刘军 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 [2]泰山双语学校,山东泰山271036 [3]黄前教育指导中心,山东泰山271036

出　　处：《模糊系统与数学》2009年第5期65-69,共5页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(10471083);陕西师范大学重点科研基金资助项目(995130)

摘　　要：讨论P-有界分配格的理想集代数与剩余格的关系。证明了在适当选取蕴涵算子及相应的剩余算子之后,P-有界分配格的理想集代数就成为剩余格。定义了生成理想,并借助格论上的原子定义了P-有界分配格,然后讨论了它的一些性质,得到了一些好的结论。最后证明了P-有界分配格的理想集代数也是MV代数与R0代数。The relation between ideal sets algebra of P-finite distributive lattice and residual lattice is studied. It is proved that ideal set algebra becomes residuai lattice if proper implication and corresponding Complement Operators are Selected.The defination of generation ideal and p-bounded distributive lattice are given,based on that and atom of lattice theory. It is prove that ideal set algebra becomes MV algebra and R0 algebra.

关 键 词：理想格 剩余格 MV代数 R0代数 

分 类 号：O141[理学—数学]