Krull-Tropical Hypersurfaces
Fuensanta Aroca · Annales de la faculté des sciences de Toulouse Mathématiques · 2011
The concepts of tropical semiring and tropical hypersurface, are extended to the case of 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.