有界Heyting代数的扩张理想和稳定理想
Expand ideals and stable ideals in bounded Heyting algebras
刘春辉1
作者信息
- 1. 赤峰学院教育科学学院,内蒙古赤峰 024001
- 折叠
摘要
运用泛代数的方法和原理深入研究有界Heyting代数的理想问题.在有界Heyting代数(H,≤,→,0,1)中引入了理想I关于H的子集的扩张理想和稳定理想概念,获得了它们的若干基本性质.系统讨论了由两类特殊扩张理想构成集合的格论特征,证明了:(1)有界Heyting代数(H,≤,→,0,1)的一个给定理想I关于H的所有子集的扩张理想全体之集EI(P(H))在一定条件下构成一个分配完备格,进一步构成一个Stone格和完备Heyting代数;(2)有界Heyting代数(H,≤,→,0,1)的关于一个给定子集A ⊆ H的稳定理想全体之集SId(H)(A)构成一个完备Heyting代数.最后考察了商有界Heyting代数和乘积有界Heyting代数的扩张理想性质.
Abstract
In this paper,the problem of ideals is studied in bounded Heyting algebras by using the principle and method of universal algebra.The notions of expand ideals and stable ideals of an ideal I associated to a subset A of bounded heyting algebra(H,≤,∨,∧,→,0,1)are introduced and some their basic properties are obtained.The lattice theory characteristics about two types sets of expand ideals in a bounded heyting algebra(H,≤,∨,∧,→,0,1)are discussed.It's proved that(1)the set EI(P(H))of all expand ideals of a given ideal I associated to any subset of H is formed a bounded distributive lattice,further formed a Stone lattice and complete Heyting algebra under certain conditions.(2)the set SId(H)(A)of all stable ideals associated to a given subset A ⊆ H is formed a complete Heyting algebra.Finally,some properties of expand ideals of quotient and product bounded Heyting algebras are investigated.
关键词
有界Heyting代数/理想/扩张理想/稳定理想/Stone格/完备Heyting代数Key words
bounded Heyting algebra/ideal/expand ideal/stable ideal/Stone lattice/complete Heyting algebra引用本文复制引用
基金项目
内蒙古自治区高等学校科研项目(NJZY21138)
内蒙古自治区高等学校科研项目(NJZY22146)
内蒙古自治区残疾人联合会研究项目(2023KTYJ19)
赤峰学院教育教学研究重点项目(2022)(JYJXZ202204)
出版年
2024
NETL
NSTL
万方数据