The quasi-Zariski topology-graph on the maximal spectrum of modules over commutative rings

Abstract

Let M be a module over a commutative ring and let Max(M) be the collection of all maximal submodules of M. We topologize Max(M) with quasi-Zariski topology, where M is a Max-top module. For a subset T of Max(M), we introduce a new graph G(τT*m)$G(\tau_T^{*m})$, called the quasi-Zariski topology-graph on the maximal spectrum of M. It helps us to study algebraic (resp. topological) properties of M (resp. Max(M)) by using the graphs theoretical tools.

Keywords

• prime submodule
• max-top module
• quasi-zariski topology
• maximal submodule
• graph
• vertices
• annihilating-submodule
• 13c13
• 13c99