Fantastic and associative filters in pseudo quasi-ordered residuated systems

Authors

DOI:

https://doi.org/10.14393/BEJOM-v4-2023-67770

Keywords:

Quasi-ordered residuated system (QRS), Pseudo-QRS, Filters in pseudo-QRS, Fantastic filter in pseudo QRS, Associative filter in pseudo QRS

Abstract

An interesting generalization of hoop-algebras and commutative residuated lattices is the concept of quasi-ordered residuated systems (shortly QRS) introduced in 2018 by Bonzio and Chajda. Quasi-ordered residuated system is an integral commutative monoid with two internal binary operations interconnected by a residuation connection. This specificity is the reason for the complexity of this algebraic structure and the existence of a significant number of substructures in it, such as various types of filters. The notion of pseudo quasi-ordered residuated systems was introduced and developed in 2022 by this author, omitting the commutativity requirement in QRSs, discussing, additionally, filters in it. Concept of pseudo QRSs is a generalization of the notion of QRSs. In this report, as a continuation of previous research, in addition to the introduction of concepts of fantastic and associative filters in a pseudo quasi-ordered residuated system, their mutual connection between them is discussed, and some examples are presented.

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Author Biography

Daniel A. Romano, IMVI Banja Luka, Bosnia and Herzegovina

Daniel A. Romano was born in Visegrad, Bosnia and Herzegovina, where he finished primary (Elementary and Middle) and High school. At the Department of Mathematics of the Faculty of Sciences, University of Sarajevo ended the undergraduate studies in mathematics and physics (1969 - 1973) and graduate studies in mathematics (1976-1978). Doctorate in mathematics defended at the Faculty of Mathematics, University of Belgrade in 1986.

In the period 1978th-2017th crossed the teaching and scientific vocation of senior assistant (1978) to full professor (1997). He was a founder of the Mathematical Society of the Republic of Srpska (1994). He is also a member of the Scientific Society of Mathematicians Banja Luka (president), the International Mathematical Virtual Institute (general manager), European Mathematical Society and the International Mathematical Union. He was a mentor to several doctoral dissertations in mathematics and a large number of master works in the field of research in mathematics education. 

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Published

2023-09-13

How to Cite

ROMANO, D. A. Fantastic and associative filters in pseudo quasi-ordered residuated systems. BRAZILIAN ELECTRONIC JOURNAL OF MATHEMATICS, Uberlândia, v. 4, p. 1–17, 2023. DOI: 10.14393/BEJOM-v4-2023-67770. Disponível em: https://seer.ufu.br/index.php/BEJOM/article/view/67770. Acesso em: 23 nov. 2024.

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Section

Articles - Pure Mathematics