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 \(S^m\)
, and provide an algebraic invariant - the \(\Lambda\)
-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)