正则FI-代数的刻画及成为Boole代数的条件

doi:10.3778/j.issn.1002-8331.1706-0345

计算机工程与应用 ›› 2018, Vol. 54 ›› Issue (16): 59-62.DOI: 10.3778/j.issn.1002-8331.1706-0345

正则FI-代数的刻画及成为Boole代数的条件

凌雪岷1，徐罗山2，杨凌云3

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

出版日期:2018-08-15 发布日期:2018-08-09

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

LING Xuemin1, XU Luoshan2, YANG Lingyun3

1.Department of Common Education, Anhui Xinhua University, Hefei 230011, China
2.College of Mathematical Science, Yangzhou University, Yangzhou, Jiangsu 225002, China
3.School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China

Online:2018-08-15 Published:2018-08-09

摘要/Abstract

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。

关键词: FI-代数, 正则FI-代数, 蕴涵分配性, Boole代数

Abstract: 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.

Key words: FI-algebra, regular FI-algebra, implicative distributivity, Boolean algebra

凌雪岷1，徐罗山2，杨凌云3. 正则FI-代数的刻画及成为Boole代数的条件[J]. 计算机工程与应用, 2018, 54(16): 59-62.

LING Xuemin1, XU Luoshan2, YANG Lingyun3. Characterizations of regular FI-algebras and condition for them to be Boolean algebras[J]. Computer Engineering and Applications, 2018, 54(16): 59-62.

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

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