JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (5): 71-80.doi: 10.6040/j.issn.1671-9352.0.2020.031

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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

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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

CLC Number: 

  • O153.2
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