Classification of Tropical Semi-Modules

Authors: Wagneur Edouard

Abstract:

Tropical algebra is the algebra constructed over an idempotent semifield S. We show here that every m-dimensional tropical module M over S with strongly independent basis can be embedded into Sm, and provide an algebraic invariant -the Γ-matrix of M- which characterises the isomorphy class of M. The strong independence condition also yields a significant improvement to the Whitney embedding for tropical torsion modules published earlier We also show that the strong independence of the basis of M is equivalent to the unique representation of elements of M. Numerous examples illustrate our results.

Keywords: classification, idempotent semi-modules, strong independence, tropical algebra