Galois connections and modal algebras

We investigate the properties of a modal algebra, more specifically, a non-distributive lattice with operators via Galois connections. Pairs of Galois are very common in mathematical environments, and, in this article, they appear as unary operators in lattices even without the distributivity. In a previous paper, Castiglioni and Ertola-Biraben studied the meet-complemented lattices with two modal operators for necessary □ and possible ◊. We observed that this pair of operators determines an adjunction. Then, we used Galois pairs on the meet-complemented lattices, showing some properties of this structure that were already been proved in their paper, and some new laws non presented. Lastly, we define a new pair of operators that also constitute another Galois pair.