Range residuated mappings (Q1089012)

If A, B are ordered sets then a mapping \(f: A\to B\) is said to be range residuated if it induces a residuated map from A to the filter generated by its range. Such mappings arise in connection with digital pictures. Various properties of range residuated mappings are given, these being generalizations of properties of residuated mappings. The link between Baer semigroups and lattices, forged by residuated mappings, is then generalized. This is achieved through the analogous notion of a Baer LZ- semigroup (in which there appears a one-sided zero element). This leads to a coordinatization of lattices by a Baer LZ-semigroup.