G-2017-44
The embedding theorem for tropical modules
BibTeX reference
Tropical algebra is the algebra constructed over the tropical semifield \(R_{max}= (R\cup \{-\infty\},\max, +)\)
. We show here that every \(m\)
-dimensional tropical module \(M\)
over \(R_{max}\)
, given by a \(n\times p\)
matrix \(A\)
can be embedded into \(R_{max}^n\)
, iff \(n\)
of its rows are independent. This result yields a significant improvement to the Whitney embedding for tropical torsion modules published earlier.
Published May 2017 , 10 pages
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G1744.pdf (300 KB)