Group for Research in Decision Analysis


Moduloids and Pseudomodules 3. Finite Dimensional Simple Pseudomodules are Lattices

We determine here sufficient conditions for finite dimensional moduloïds and pseudomodules to be lattices. As could be expected, completeness of the scalar dioïd D is such a condition. More interestingly, the simplicity conditions for pseudomodules, which make the classification problem tractable in the finite dimensional case, are also shown to be sufficient for the lattice structure. These two sets of sufficient conditions being unrelated, we conclude that neither condition is necessary. A final example slightly generalizes this remark.

, 14 pages

This cahier was revised in March 1990