Let M be a module over a commutative ring R. In this paper, we introduce the notion of M-strongly irreducible ideals of R. We use this type of ideals to define a topology relative to ring R and R-module M. We investigate the relationship between algebraic properties of M and R and also, we study topological properties of the topology on the set of all M-strongly irreducible ideals of R. Moreover, modules whose topologies are  irreducible or Noetherian are studied.