Galois connection of stabilizers in residuated lattices

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 $\mathfrak{A}$ is a residuated lattice and $F$ be a filter of $\mathfrak{A}$ we show that the set of all stabilizers relative to $F$ of a same type forms a complete lattice. Furthermore, we prove that $ST-F_{l}^{\square}$, $ST-F_{l}$ and $ST-F_{s}$ are pseudocomplemented lattices.