The concept of idempotent semiring module is a generalisation of
the so-called Max-algebra (or tropical algebra) widely used in the the-
ory and control of discrete event system.
The classication of modules over a principal ideal domains is given
by their decomposition into a direct sum of free and torsion modules.
No such result exists for idempotent semimodules over an idempotent
semring (or semield). This is essentially due to the fact that the direct
sum decomposition of tidempotent semimodules is trivial, on the one
hand, and that this classication problem received scant attention in
the other. In fact, for a given (idempotent) semimodule M, we would
like do fnd algebraic invariants which characterise the isomorphy class
of M. We will state here a necessary and sucient for such algebraic
invariant to exist for a subclass of general idempotent semimodules:
(idempotent) semimodules with strongly independent basis.