格的正规完备化的Boolean性  

Boolean Properties of Normal Completions of Lattices

作　　者：江碧霞 徐晓泉[1] JIANG Bi-xia;XU Xiao-quan(College of Math.and In formation Sci.,Jiangxi Normal University,Nanchang 330022,China)

机构地区：[1]江西师范大学数学与信息科学学院

出　　处：《模糊系统与数学》2019年第6期161-164,共4页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11661057);“赣鄱英才555工程”领军人才培养计划项目;江西省自然科学基金资助项目(20192ACBL20045)

摘　　要：引入了E-Heyting偏序集和伪补交半格的概念,证明了若B=(B,∨,∧,0,1)为有0,1的格,则B为Boolean代数当且仅当B为Heyting且其正规完备化为Boolean代数,当且仅当B为伪补交半格且其正规完备化为Boolean代数。In this paper,the concepts of E-Heyting posets and pseudocomplement semilattices are introduced.It is proved that if B=(B,∨,∧,0,1)is a lattice with 0 and 1,then B is a Boolean algebra if and only if B is a Heyting and让s normal completion is a Boolean algebra if and only if B is a pseudocomplement semilattice and its normal completion is a Boolean algebra.

关 键 词：Boolean代数 HEYTING代数 正规完备化 

分 类 号：O159[理学—数学]