Frontal operators in distributive lattices with a generalized implication

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 in [4]. 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 ([9]). In particular, we study the case of frontal gi-lattices where the generalized implication is defined as the annihilator ([11], [15]). We give a Priestley’s style duality for each one of the new classes of structures considered.Fil: Celani, Sergio Arturo. Universidad Nacional del Centro de la Provincia de Buenos Aires.Facultad de Ciencias Exactas; ArgentinaFil: San Martín, Hernán Javier. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin