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 S...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（R）, and investigate this topolog- ical space. For various types of modules M, we obtain conditions under which Spec^S（M） is a spectral space. We also investigate Specs （M） with quasi-Zariski topology.展开更多
文摘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（R）, and investigate this topolog- ical space. For various types of modules M, we obtain conditions under which Spec^S（M） is a spectral space. We also investigate Specs （M） with quasi-Zariski topology.
