SECOND CLASSICAL ZARISKI TOPOLOGY ON SECOND SPECTRUM OF LATTICE MODULES

Let M be a lattice module over a C-lattice L. Let Spec(s)(M) be the collection of all second elements of M. In this paper, we consider a topology on Spec(s)(M), called the second classical Zariski topology as a generalization of concepts in modules and investigate the interplay between the algebraic properties of a lattice module M and the topological properties of Spec(s)(M). We investigate this topological space from the point of view of spectral spaces. We show that Spec(s)(M) is always T-0-space and each finite irreducible closed subset of Spec(s)(M) has a generic point.