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

L'Algebre Tropicale Comme Algebre De la Caracteristique 1 : Polynomes Rationnels Et Fonctions Polynomiales