  Much like in the theory of algebraic geometry, we develop a correspondence
between certain types of algebraic and geometric objects. The basic algebraic
environment we work in is the a semifield of fractions H(x1,...,xn) of the
polynomial semidomain H[x1,...,xn], where H is taken to be an idempotent
semifield, while for the geometric environment we have the space H^n. We show
that taking H to be idempotent makes both H(x1,...,xn) and Hn idempotent which
turn out to satisfy many desired properties that we utilize for our
construction. The fundamental algebraic and geometric objects having
interrelations are called kernels, encapsulating congruences over semifields
and skeletons which serve as the analog for zero-sets of algebraic geometry. As
an analog for the celebrated Nullstellenzats theorem, we develop a
correspondence between skeletons and a family of kernels called polars
originally developed in the theory of lattice-ordered groups. For a special
kind of skeletons, called principal skeletons, we have simplified the
correspondence by restricting our algebraic environment to a certain kernel of
H(x1,...,xn). After establishing the linkage between kernels and skeletons we
proceed to construct a second linkage, this time between a family of skeletons
and what we call "corner-loci". Essentially a corner locus is what is called a
tropical variety in the theory of tropical geometry, which is a set of corner
roots of some set of tropical polynomials. A skeleton and a corner-locus define
the exact same subset of H^n in different ways: while a corner locus is defined
by corner roots of tropical polynomials, the skeleton is defined by equating
fractions from H(x1,...,xn) to 1. All the connections presented above form a
path connecting a tropical variety to a certain kind of kernel.
