正则FI-代数的刻画及成为Boole代数的条件  

Characterizations of regular FI-algebras and condition for them to be Boolean algebras

作　　者：凌雪岷[1] 徐罗山[2] 杨凌云 LING Xuemin;XU Luoshan;YANG Lingyun(Department of Common Education,Anhui Xinhua University,Hefei 230011,China;College of Mathematical Science,Yangzhou University,Yangzhou,Jiangsu 225002,China;School of Mathematics and Statistics,Jiangsu Normal University,Xuzhou,Jiangsu 221116,China)

机构地区：[1]安徽新华学院通识教育部,合肥230011 [2]扬州大学数学科学学院,江苏扬州225002 [3]江苏师范大学数学与统计学院,江苏徐州221116

出　　处：《计算机工程与应用》2018年第16期59-62,共4页Computer Engineering and Applications

基　　金：国家自然科学基金(No.11671008;No.61300153);江苏省高校自然科学基金(No.15KJD110006);江苏高校品牌专业建设工程项目(No.PPZY2015B109;No.PPZY2015A013);安徽新华学院重点科研项目(No.2017zr011)

摘　　要：正则FI-代数是仅基于蕴涵算子在一般集合上建立的逻辑代数。基于正则FI-代数的公理组以及诸多性质之间的内部联系,给出了正则FI-代数的两个公理组条件更少的刻画定理,简化了正则FI-代数的定义形式。在正则FI-代数中引入蕴涵分配性,探讨了蕴涵分配正则FI-代数的若干性质,证明了蕴涵分配正则FI-代数与Boole代数是相互等价的代数系统,给出了Boole代数的一种新的刻画,使其在形式上更接近于二值逻辑代数。The regular FI-algebras are built up on general sets merely by the implication operation.In this paper,based on axiom groups and internal relations of properties of regular FI-algebras,two characterizations of regular FI-algebras with fewer axioms are given,which simplify the definition of regular FI-algebras.Moreover,implicative distributivity is introduced into regular FI-algebras and some properties of implicative distributive FI-algebras are discussed.It is proved that implicative distributive regular FI-algebras and Boolean algebras are equivalent algebraic structures.A new characterization for Boolean algebras is given,showing them to be more similar to two-valued logic algebras in form.

关 键 词：FI-代数 正则FI-代数 蕴涵分配性 BOOLE代数 

分 类 号：O141[理学—数学] O153[理学—基础数学]