Decompositions in Complete Lattices III. Unique Irredundant Decompositions and Convex Geometries

详细

We give a characterization of complete strongly dually atomic lattices having unique irredundant decompositions which are also canonical. It is shown that all known characterizations of lattices with unique irredundant decompositions are a consequence of this result. In addition, upper continuous closure lattices of convex geometries with (unique) irredundant decompositions are characterized.