Groupe d’études et de recherche en analyse des décisions

# The Classification Problem for Moduloids of Finite Type

## Edouard Wagneur

We study here the classification problem for a particular class of moduloïds over a dioïd, called simple pseudomodules. After introducing the concept of canonical basis, we show that the submoduloïd generated by such a basis over {0,1} completely characterizes the simple pseudomodule structure. it follows that every simple pseudomodule of dimension n is isomorphic to a pseudomodule generated by n relatively irreducible elements of the free semilattice generated by n elements, a result which parallels the standard classification theorem for modules over a ring.

We also show that, when D is discrete with no inverses, then there are infinitely many moduloïd structures of dimension n ≥ 2.

Finally we show how the moduloïd of monomials of degree n in one indeterminate can be represented as a submoduloïd of Dm, for some (minimal) mn.

, 16 pages