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Keywords:
prime submodules; multiplication modules; distributive lattices; spectral spaces
prime submodules; multiplication modules; distributive lattices; spectral spaces
Summary:
We shall prove that if $M$ is a finitely generated multiplication module and $\mathop {\mathrm Ann}(M)$ is a finitely generated ideal of $R$, then there exists a distributive lattice $\bar{M}$ such that $\mathop {\mathrm Spec}(M)$ with Zariski topology is homeomorphic to $\mathop {\mathrm Spec}(\bar{M})$ to Stone topology. Finally we shall give a characterization of finitely generated multiplication $R$-modules $M$ such that $\mathop {\mathrm Ann}(M)$ is a finitely generated ideal of $R$.
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