Advanced Search

We shall prove that if $M$ is a finitely generated multiplication module and $\mathrm{A}nn\left(M\right)$ is a finitely generated ideal of $R$, then there exists a distributive lattice $\overline{M}$ such that $\mathrm{S}pec\left(M\right)$ with Zariski topology is homeomorphic to $\mathrm{S}pec\left(\overline{M}\right)$ to Stone topology. Finally we shall give a characterization of finitely generated multiplication $R$-modules $M$ such that $\mathrm{A}nn\left(M\right)$ is a finitely generated ideal of $R$.