Open AccessImplicative filters in quasi-ordered residuated systems
Author(s) -
Daniel A. Romano
Publication year - 2021
Publication title -
proyecciones
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.226
H-Index - 12
eISSN - 0717-6279
pISSN - 0716-0917
DOI - 10.22199/issn.0717-6279-2021-02-0025
Subject(s) - monoid , residuated lattice , mathematics , commutative property , relation (database) , pure mathematics , order (exchange) , algebraic structure , identity (music) , algebraic number , type (biology) , algebra over a field , computer science , artificial intelligence , mathematical analysis , philosophy , business , data mining , ecology , finance , biology , fuzzy logic , aesthetics
The concept of residuated relational systems ordered under a quasiorder relation was introduced in 2018 by S. Bonzio and I. Chajda as a structure = 〈A, ·,→, 1, R〉, where (A, ·) is a commutative monoid with the identity 1 as the top element in this ordered monoid under a quasi-order R. The author introduced and analyzed the concepts of filters in this type of algebraic structures. In this article, as a continuation of previous author’s research, the author introduced and analyzed the concept of implicative filters in quasi-ordered residuated systems.