2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124363Let $\mathfrak{g}$ be a solvable Lie algebra and $Q$ an $ad \mathfrak{g}$-stable prime ideal of the symmetric algebra $S(\mathfrak{g})$ of $\mathfrak{g}$. If $E$ is the set of non zero elements of $S(\mathfrak{g})/Q$ which are eigenvectors for the adjoint action of $\mathfrak{g}$ in $S(\mathfrak{g})/Q$, the localised algebra $(S(\mathfrak{g})/Q)_{E}$ has a natural structure of Poisson algebra. We study this algebra here.This paper is in frenchRings and Algebras17B63text