@article{article_1376000, title={Some new results on quasi-ordered residuated systems}, journal={Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics}, volume={74}, pages={27–34}, year={2025}, DOI={10.31801/cfsuasmas.1376000}, author={Romano, Daniel A.}, keywords={Quasi-ordered residuated system, atom in quasi-ordered residuated system, extension of quasi-ordered residuated system}, 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 $\mathfrak{A}\cup\{a\}$.}, number={1}, publisher={Ankara University}