Maximal filter and its topology in lattice implication algebras

Article type: Research Article

Authors: Qin, Ya^a | Liu, Yi^{a; b; *}

Affiliations: [a] College of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan province, P.R. China | [b] Data Recovery Key Lab of Sichuan Province, Neijiang Normal University, Neijiang, Sichuan, P.R. China

Correspondence: [*] Corresponding author. Liu Yi, E-mail: liuyi@njtc.edu.cn.

Abstract: The present work aims at investigating maximal filter and its topological properties in lattice implication algebras (LIAs). To begin with, the maximal filters of LIAs are investigated and some equivalent characterizations of maximal filters are also given. In addition, the radical of filters in a LIA is introduced and its properties are also obtained, the structure of radical of maximal filter is investigated. Finally, by introducing some topological structures on the set of all maximal filters and by investigating the topological properties of them, we conclude that the set of all maximal filters is a compact topological space and the set of all maximal filters is also a Hausdorff topological space.

Keywords: Lattice implication algebra, maximal filter, radical, topology

DOI: 10.3233/JIFS-171025

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 1, pp. 673-681, 2018