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Regular version of the site

Article

Tropical semimodules of dimension two

St Petersburg Mathematical Journal. 2015. Vol. 26. P. 341-350.
Shitov Y.

In the paper, the concept of a semimodule is discussed, which is rather ill-behaved in tropical mathematics. The semimodules S in R^n  having topological dimension two are studied, and it is shown that any such S has a finite weak dimension not exceeding n. For a fixed k, a polynomial time algorithm is constructed that decides whether S is contained in some tropical semimodule of weak dimension k or not. This result provides a solution of a problem that has been open for eight years.