Three types of prime filters in strong quasi-ordered residuated system

Abstract

The concept of quasi-ordered residuated system was introduced in 2018 by Bonzio and Chajda. The author introduced and analyzed the concept of filters as well as some types of filters in such an algebraic system. Additionally, the author also dealt with a strong quasi-ordered residuated system in which he determined prime and irreducible filters. In this paper, the author introduce three types of prime filters in a strong quasi-ordered residuated system and analyze their interconnections.