Varieties of tropical ideals are balanced

Tropical ideals, introduced in [12], define subschemes of tropical toric varieties. We prove that the top-dimensional parts their varieties are balanced polyhedral complexes same dimension as ideal. This means every subscheme a variety defined by ideal has an associated class Chow ring variety. A key tool proof is specialization variables yields another ideal; this plays role hyperplane sections theory. also show elimination theory (projection varieties) works for ideals classical case. The matroid condition defines crucial these results.