Weak implicative filters in quasi-ordered residuated systems

• Romano, Daniel ^[1]
  1. [1] International Mathematical Virtual Institute.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 40, Nº. 3, 2021 (Ejemplar dedicado a: In progress (June 2021). This issue is in progress. Contains articles that are final and fully citable.), págs. 797-804
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-4332
• Enlaces
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• Resumen

  • 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 = 〈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 and implicative filters in this type of algebraic structures. In this article, the concept of weak implicative filters in a quasi-ordered residuated system is introduced as a continuation of previous researches. Also, some conditions for a filter of such system to be a weak implicative filter are listed.

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