Geodesic
On finitely generated multiplication modules
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 503-510
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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 $R$.
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 $R$.
Classification : 06B10, 13A15, 13C13, 13C99
Keywords: prime submodules; multiplication modules; distributive lattices; spectral spaces 
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     title = {On finitely generated multiplication modules},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a20/}
}
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Nekooei, R. On finitely generated multiplication modules. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 503-510. http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a20/

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