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《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (5): 71-80.doi: 10.6040/j.issn.1671-9352.0.2020.031

• • 上一篇    

Heyting代数的布尔原子及其应用

赵马盼,樊丰丽,颉永建*   

  1. 陕西师范大学数学与信息科学学院, 陕西 西安 710062
  • 发布日期:2020-05-06
  • 作者简介:赵马盼(1997— ), 女, 硕士研究生, 研究方向为量子逻辑. E-mail:1151034980@qq.com *通信作者简介:颉永建(1978— ), 男, 副教授, 硕士生导师, 研究方向为量子逻辑. E-mail:yjxie@snnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(61673250);陕西省自然科学基础研究计划(2020JM-274);中央高校基本科研业务费重点项目(GK201902004)

Boolean atoms of Heyting algebras and their application

ZHAO Ma-pan, FAN Feng-li, XIE Yong-jian*   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China
  • Published:2020-05-06

摘要: 利用Heyting代数的布尔元得到了Heyting代数的一种直积分解表示。基于Heyting代数的这种分解,证明了有限Heyting代数可通过依次替换布尔代数中的原子为Heyting代数而得到。该结论揭示了Heyting代数与布尔代数之间的一种新的关系。

关键词: Heyting代数, 布尔代数, 布尔原子, 替换

Abstract: A kind of direct product decomposition of Heyting algebras is obtained using the Boolean elements of Heyting algebras. Based on this decomposition of Heyting algebras, it is proved that a finite Heyting algebra can be obtained by substituting the atoms of a Boolean algebra with Heyting algebras. This conclusion reveals a kind of new relationship between Heyting algebras and Boolean algebras.

Key words: Heyting algebra, Boolean algebra, Boolean atom, substitution

中图分类号: 

  • O153.2
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