非全序R_0代数的存在性及其构造  

Existence of non-totally ordered R_0-algebras and their construction

作　　者：韩诚[1] 许文艳[1] 吴恒洋[2] 

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]上海师范大学数理信息学院,上海200234

出　　处：《陕西师范大学学报（自然科学版）》2004年第1期25-28,共4页Journal of Shaanxi Normal University：Natural Science Edition

摘　　要：通过考察非全序R0代数的序结构,给出了中点的定义,并利用中点给出R0代数的一个分划,同时证明了五元和七元非全序R0代数不存在,以及n元(n>7)非全序R0代数的存在性,并推广到无限元的情形,得到了构造可去(加)中点的非全序R0代数的两种方法.Through investigating the order structure of non-totally ordered R_0-algebra, this is given that the definition of middle point and obtains a partition of the set of R_0-algebras by making use of middle point. It is proved that that 5-ary and 7-ary non-totally ordered R_0-algebras don′t exist, however, n-ary one exists, ((n>7)). Furthermore, the existence of infinite non-totally ordered R_0(-algebras) is proved, and two constructions of non-totally ordered R_0-algebras whose middle point is removable or additive are given.

关 键 词：非全序R0代数 序结构 中点 L-Lindenbaum代数 模糊逻辑 命题演算 

分 类 号：O141.1[理学—数学] O159[理学—基础数学]