Galois connection of stabilizers in residuated lattices, By Saeed Rasoli

Research

Title	Galois connection of stabilizers in residuated lattices
Type	Article
Keywords	residuated lattice, filter; stabilizer, Galois connection, complete lattice, pseudocomplemented lattice
Journal	Filomat
DOI	https://doi.org/10.2298/FIL2004223R
Researchers	Saeed Rasoli (First researcher)

Abstract

The paper is devoted to introduce the notions of some types of stabilizers in non-commutative residuated lattices and to investigate their properties. We establish a connection between (contravariant) Galois connection and stabilizers of a residuated lattices. If A is a residuated lattice and F be a filter of A, we show that the set of all stabilizers relative to F of a same type forms a complete lattice. Furthermore, we prove that ST − F, ST − Fl and ST − Fs are pseudocomplemented lattices.