HYPER QUASI-ORDERED RESIDUATED SYSTEMS - Romano, Daniel Abraham (Matematichki Bilten, 2023)
The concept of quasi-ordered residuated systems as a generalization of both quasi-ordered residuated lattices and hoop-algebras was developed in 2018 by Bonzio and Chajda. In this paper, we apply the hyper structure theory to quasi-ordered residuated systems and we introduce the notion of hyper quasi-ordered residuated system which is a generalization of quasi-ordered residuated systems on the one hand and a generalization of both hyper quasi-ordered residuated lattices and hyper hoop-algebra, on the other hand, and we investigate some of their related properties. In addition to the previous one, the concept of deductive systems and concept of filters in this algebraic structure are presented and analyzed as well as the connections between them.