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

Daniel A. Romano1

International Mathematical Virtual Institute, 6, Kordunaska Street, 78000 Banja Luka, Bosnia and Herzegovina.

* Corresponding Author

Annals of Communications in Mathematics 2023

, 6 (3),

199-208.

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

Received: 04 September 2023 |

Accepted: 22 October 2023 |

Published: 31 October 2023

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Abstract
The 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.

Keywords

Correspondence filter and ideal induced by a quasi-valuation; Quasi-ordered redisuated system (shortly QRS); Quasi-valuation map on QRS; Quotient QRS

Cite This Article

Daniel A. Romano1

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

Annals of Communications in Mathematics,

2023,

6 (3):

199-208.

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

Copyright © 2024 by the Author(s). Licensee Techno Sky Publications. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).