  We continue, in this second article, the study of the the algebraic tools
which play a role in tropical algebra. We especially examine here the
polynomial algebras over idempotent semi-fields. this work is motivated by the
development of tropical geometry which appears to be the algebraic geometry of
tropical algebra. In fact, the most interesting object is the image of a
polynomial algebra in its semi-field of fractions. We can thus obtain, over
good semi-fields, the analog of classical correpondences between polynomials,
and varieties of zeros... For example, we show that the algebras of polynomial
functions over a tropical curves associated to a polynomial P, is, as in
classical algebraic geometry, the quotient of the polynomial algebra by the
ideal generated by P.
