  The concepts of tropical-semiring and tropical hypersurface, are extended for
an arbitrary ordered group. Then, we define the tropicalization of a polynomial
with coefficients in a Krull-valued field. After a close study of the
properties of the operator "tropicalization" we conclude with an extension of
Kapranov's theorem to algebraically closed fields together with a valuation
over an ordered group.

Algebraic Geometry;Commutative Algebra