Frontal operators in distributive lattices with a generalized implication

SERGIO ARTURO CELANI; SAN MARTÍN HERNÁN JAVIER

Asian-European Journal of Mathematics (AEJM)

China

Año: 2015 vol. 8

1793-5571

We introduce a family of extensions of bounded distributive lattices. These extensions are obtained by adding two operations: an internal unary operation, and a function (called generalized implication) that maps pair of elements to ideals of the lattice. A bounded distributive lattice with a generalized implication is called gi-lattice. The main goal of this paper is to introduce and study the category of frontal gi-lattices (and some subcategories of it). This category can be seen as a generalization of the category of frontal weak Heyting algebras. In particular, we study the case of frontal gi-lattices where the generalized implication is defined as the annihilator. We give a Priestley´s style duality for each one of the new classes of structures considered.