Home 9 Author: Daniel A. Romano
Daniel A. Romano
Open AccessArticle

Quotient quasi-ordered residuated systems induced by quasi-valuation maps

Annals of Communications in Mathematics 2023

, 6 (3)

, 199-208

DOI: https://doi.org/10.62072/acm.2023.060305

AbstractThe concept of quasi-ordered residuated systems was introduced in 2018 by Bonzio and Chajda as a generalization both of commutative residuated lattices and hoopalgebras. Then this author investigated the substructures of ideals and filters in these algebraic structures. As a continuation of these research, in this article we design the concept of quotient quasi-ordered residuated systems induced by a quasi-valuation on it. Additionally, we prove some important properties of the thus constructed quotient structure.

Open AccessArticle

Implicative strong filters in hyper quasi-ordered residuated systems

Annals of Communications in Mathematics 2023

, 6 (2)

, 86-98

DOI: https://doi.org/10.62072/acm.2023.060202

AbstractQuasi-ordered residuated systems as a generalization of both quasi-ordered commutative residuated lattices and hoop-algebras were developed in 2018 by Bonzio and Chajda. The ideas of the theory of hyper structures were applied to this algebraic structure by this author and, at the same time, developed the concepts of filters in a hyper quasi-ordered residuated system. In this paper, the conditions that determine the concept of implicative strong filters in it. Some equivalent conditions were found that also determine this concept.