Some new results on quasi-ordered residuated systems

Year 2025, Volume: 74 Issue: 1, 27 - 34

Daniel A. Romano

Abstract

Quasi-ordered residuated system is a commutative residuated integral monoid ordered under a quasi-order was introduced in 2018 by Bonzio and Chajda as a generalization of commutative residuated lattices and hoop-algebras. This paper introduces the concept of atoms in these systems and analyzes its properties. Additionally, two extensions of the system $\mathfrak{A}$ to the system $\mathfrak{A}\cup\{a\}$ were designed so that the element $w$ is an atom in $\mathfrak{A}\cup\{a\}$.

Keywords

Quasi-ordered residuated system, atom in quasi-ordered residuated system, extension of quasi-ordered residuated system

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