A Zariski Topology on the Primary-like Spectrum of ν-Multiplication Modules

Let R be a commutative ring with identity and M be a unitary R-module. Primary-like spectrum of M is the set of all primary-like submodules of M . In this paper, we introduce a class of modules, called ν-multiplication modules, which their primary-like spectrum has a Zariski topology. We show that if R is a Notherian ring, M a ν-multiplication R-module and T the Zariski topology for the primary-like spectrum X of M , then (X , T ) is a Noetherian space.