Pseudo Quasi-Ordered Residuated Systems, An Introduction

Daniel A. Romano

Abstract

The concept of quasi-ordered residuated systems was introduced in 2018 by S. Bonzio and I. Chajda as a generalization of both hoop-algebras and commutative residuated lattices ordered by quasi-orders. The substructures of ideals and filters in such algebraic structures were considered by the author. This paper introduces and analyzes the concept of pseudo quasi-ordered residuated systems as a non-commutative generalization of quasi-ordered residuated systems with left and right residuum operations. Also, this paper discusses the concepts of ideals and filters in pseudo quasi-ordered residuated systems.

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Pan-Amer. J. Math. 1 (2022), 12
DOI: https://doi.org/10.28919/cpr-pajm/1-12
This article was published on August 23, 2022 by Mathyze, under a Creative Commons Attribution 4.0 International License.