@article { author = {Ansari-Toroghy, H. and Ovlyaee-Sarmazdeh, R. and Pourmortazavi, Seyed Sajad}, title = {On two problems concerning the Zariski topology of modules}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {42}, number = {4}, pages = {941-948}, year = {2016}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, abstract = {Let $R$ be an associative ring and let $M$ be a left $R$-module. Let $Spec_{R}(M)$ be the collection of all prime submodules of  $M$ (equipped with classical Zariski topology). There is a conjecture  which says that every irreducible closed subset of $Spec_{R}(M)$ has a generic point. In this article we give an affirmative answer to this conjecture and show that if $M$ has a Noetherian spectrum, then $Spec_{R}(M)$ is a spectral space.}, keywords = {Prime spectrum,classical Zariski topology,spectral space}, url = {http://bims.iranjournals.ir/article_846.html}, eprint = {http://bims.iranjournals.ir/article_846_1769c60f5d1f171166300f224d7e2683.pdf} }