Ideals in quasi-ordered residuated system
Daniel A. Romano · Contributions to Mathematics · 2021
The concept of quasi-ordered residuated system was defined in 2018 by Bonzio and Chajda.The present author defined the notion of filters in quasi-ordered residuated system and described several different classes of filters in such systems.In this paper, the concept of pre-ideals and ideals in a residuated relational system ordered under a quasi-order are introduced and analyzed.Some important features of these classes of substructures in such relational systems are also shown.In addition, a congruence relation based on the concept of pre-ideal is constructed.