On the Zariski topology over an L-module M

Abstract

Let L be a multiplicative lattice and M be an L-module. In this study, we present a topology said to be the Zariski topology over sigma(M), the collection of all prime elements of an L-module M. We research some results on the Zariski topology over sigma(M). We show that the topology is a T-0-space and a T-1-space under some conditions. Some properties and results are studied for the topology over sigma-(L), the collection of all prime elements of a multiplicative lattice L.