Distributivity and irreducibility in closure systems

Preprint enviat per a la seva publicació en una revista científica.In this work we see how the property: T V (S(x) ∩ S(y)) = (T V S (x)) ∩ (t V S (y)) where T is a closed set of the closure system associated to the closure to the operator S, is related to the distributivity of the closure system's lattice and to a claracterization of the irreducible closed sets