On the Maximal Spectrum of a Module and Zariski Topology

For any module Mover a commutative ring R, Spec(R)(M) (resp. Max(R)(M)) of M is the collection of all prime (resp. maximal) submodules. In this article, we investigate the interplay between the topological properties of Max(R)(M) and module theoretic properties of M. Also, for various types of modules M, we obtain some conditions under which Max(R)(M) is homeomorphic with the maximal ideal space of some ring.