Filter theory of pseudo equality algebras

Article type: Research Article

Authors: Liu, Meng Ke^a | Xin, Xiao Long^{a; b; *}

Affiliations: [a] School of Mathematics, Northwest University, Xi’an, China | [b] School of Science, Xi’an Polytechnic University, Xi’an, China

Correspondence: [*] Corresponding author. Xiao Long Xin. Tel.: +86 13571952880; E-mails: xlxinxa@126.com and xlxin@nwu.edu.cn

Abstract: In this paper, we study the generating formula of filters in pseudo equality algebras, also we introduce prelinear pseudo equality algebras and divisible pseudo equality algebras, and then we investigate some characterizations of them. We focus on algebraic structures of the set F (X) of all filters in pseudo equality algebras and obtain that F (X) can form a Heyting algebra. Moreover, we give the notions of some types of filters ((positive) implicative filters, fantastic filters) in pseudo equality algebras and investigate their properties. Finally, we discuss the relations among these filters.

Keywords: Pseudo equality algebra, prelinear pseudo equality algebra, divisible pseudo equality algebra, (positive) implicative filter, fantastic filter, strong normal filter

DOI: 10.3233/JIFS-191512

Journal: Journal of Intelligent & Fuzzy Systems, vol. 39, no. 1, pp. 475-487, 2020