格蕴涵代数的素对偶理想  

Prime Dual Ideals of Lattice Implication Algebra

作　　者：王学芳[1] 刘培顺[2] 徐扬[3] 

机构地区：[1]中国海洋大学数学系,山东青岛266071 [2]中国海洋大学计算机系,山东青岛266071 [3]西南交通大学智能控制开发中心,四川成都610031

出　　处：《模糊系统与数学》2006年第5期37-42,共6页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(60474022)

摘　　要：在格蕴涵代数中定义了一类特殊的素对偶理想,讨论了它们的结构和性质,证明了该格蕴涵代数中的蕴涵运算可以由这些特殊的素对偶理想所确定,并且这些特殊的素对偶理想全体自然地构成一个格蕴涵代数,它和原格蕴涵代数具有格蕴涵代数同构关系。A special kind of prime dual ideals are defined in a lattice implication algebra, then their structures and properties are discussed. It is proved that the implication operation on this lattice implication algebra is determined by these prime dual ideals, and all of these prime dual ideals compose a lattice implication algebra which is lattice implication isomorphic to the former lattice implication algebra.

关 键 词：非经典逻辑 格值逻辑 格蕴涵代数 对偶理想 素对偶理想 滤子 

分 类 号：O159[理学—数学]