Fantastic and associative filters in pseudo quasi-ordered residuated systems

Autores

DOI:

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

Palavras-chave:

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

Resumo

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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Biografia do Autor

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

Daniel A. Romano nasceu em Visegrad, Bósnia e Herzegovina, onde concluiu o ensino fundamental (elementar e médio) e o ensino médio. Na Faculdade de Matemática da Faculdade de Ciências da Universidade de Sarajevo, ele concluiu seus estudos de graduação em matemática e física (1969 - 1973) e seus estudos de pós-graduação em matemática (1976-1978). Ele defendeu seu doutorado em matemática na Faculdade de Matemática da Universidade de Belgrado em 1986.

No período de 1978 a 2017, ele avançou em sua carreira acadêmica, começando como assistente sênior em ensino e pesquisa (1978) e alcançando a posição de professor titular (1997). Ele foi um dos fundadores da Sociedade Matemática da República da Srpska em 1994 e atualmente é membro e presidente da Sociedade Científica de Matemáticos de Banja Luka, bem como o gerente geral do Instituto Matemático Virtual Internacional. Além disso, ele é membro da Sociedade Matemática Europeia e da União Matemática Internacional. Romano também desempenhou o papel de orientador em várias teses de doutorado em matemática e em um grande número de trabalhos de mestrado na área de pesquisa em educação matemática.

Referências

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Publicado

2023-09-13

Como Citar

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: 12 jun. 2024.

Edição

Seção

Artigos - Matemática Pura