CSKI seminar: Classification of idempotent semiring modules with strongly independent basis

The concept of idempotent semiring module is a generalisation of the so-called Max-algebra (or tropical algebra) widely used in the theory and control of discrete event system. The classification 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 semifield). This is essentially due to the fact that the direct sum decomposition of tidempotent semimodules is trivial, on the one hand, and that this classification 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 sufficient for such algebraic invariant to exist for a subclass of general idempotent semimodules: (idempotent) semimodules with strongly independent basis.