摘要
运用泛代数和格理论的方法和原理研究有界Heyting代数及其理想问题。首先,给出了有界Heyting代数的若干新性质。其次,在有界Heyting代数(H,≤,→,0,1)中引入理想及由H的非空子集生成的理想概念并考察它们的性质和刻画。再次,分析了H的理想与格理想以及滤子三个概念之间的关系。最后,讨论了H的全体理想之集ID(H)的格结构特征,证明了ID(H)在集合包含序?下构成完备Heyting代数和分配的连续(代数)格,进而构成一个Frame.
In this paper,bounded Heyting algebras and its ideals problem is studied by using the principle and method of universal algebras and lattice theory.Firstly,some properties of bounded Heyting algebras are given.Secondly,the notions of ideals and ideal generated by a non-empty subset of H are introduced in bounded Heyting algebra(H,≤,→,0,1),and some of their properties and equivalent characterizations are investigated.Then,the relations between ideals and lattice ideals and filters in H are analyzed.Finally,the lattice structure of the set ID(H)consisting of all ideals in H is discussed,it is proved that ID(H)forms a complete Heyting algebra and a distributive continuous(algebraic)lattice under set-inclusion order?,and particularly forms a frame.
作者
刘春辉
LIU Chun-hui(School of Education,Chifeng University,Chifeng 024001,China)
出处
《模糊系统与数学》
北大核心
2022年第5期54-68,共15页
Fuzzy Systems and Mathematics
基金
内蒙古自治区高等学校科学研究项目(NJZY21138)。
