On the Zariski topology over an LL-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 σ(M), the collection of all prime elements of an L-module M. We research some results on the Zariski topology over σ(M). We show that the topology is a T0 -space and a T1 -space under some conditions. Some properties and results are studied for the topology over σ(L), the collection of all prime elements of a multiplicative lattice L.