The zariski topology on the second spectrum of a module

چکیده مقاله

Let R be a commutative ring and M be an R-module. The second spectrum Spec^s(M) of M is the collection of all second submodules of M. We topologize Spec^s(M) with Zariski topology, which is analogous to that for Spec(M), and investigate this topological space. For various types of modules M, we obtain conditions under which Spec^s(M) is a spectral space. We also investigate Spec^s(M) with quasi-Zariski topology. © 2014 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and Suzhou University.