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G-2014-23

Classification of idempotent semi-modules with strongly independent basis

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We show here that every m-dimensional semiring module M over an idempotent semiring S with strongly independent basis can be embedded into Sm, and provide an algebraic invariant - the Λ-matrix - 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 [LAA 435, 1786-1795, 2011]. 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, and a fast test for strong independence of the columns of a matrix is provided.

, 12 pages

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G1423.pdf (400 KB)