  Tropical geometry is a degeneration of classical geometry which loose the
property of unique factorization for polynomials. In this paper we explore a
structure that is known to be a semi-degeneration between the classical algebra
and the tropical algebra, and show that unique factorization fails in several
variables due to geometric reasons, not just algebraic. We also show that
unique factorization does hold for a certain interesting subset of polynomials.
