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Regular version of the site

Article

Tropical semimodules of dimension two

St Petersburg Mathematical Journal. 2014. Vol. 26. No. 2. P. 216-228.
Shitov Y.

The tropical arithmetic operations on R are defined as (a,b) -> min{a,b} and (a,b) -> a+b. We are interested in the concept of a semimodule, which is rather ill-behaved in tropical mathematics. In our paper we study the semimodules S in R^n having topological dimension two, and we show that any such S has always a finite weak dimension not exceeding n. For a fixed k, we construct a polynomial time algorithm deciding whether S is contained in some tropical semimodule of weak dimension k or not. The latter result
provides a solution of a problem that has been open for eight years.