G-2014-23
Classification of idempotent semi-modules with strongly independent basis
BibTeX reference
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.
Published April 2014 , 12 pages
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G1423.pdf (400 KB)