On intersection graph of intuitionistic fuzzy submodules of a module

Abstract

There are some interesting relations between submodules of a module and its intuitionistic fuzzy (IF) submodules. In this paper we investigate some relationshipsbetween submodules of a module and its IFsubmodules. Then we introduce a graph structure on IFsubmodules of a module and obtain some properties of it, that is the main goal of this paper. We define the intersection graph of submodules of a module M(G) and we show that a submodule Nof Mis a center in MGif and only if IFNis a center in IFG. We get some relationships between IFsubmodules of a module and their supports, as vertices of IFgraph and crisp graph of a module M, respectively. We show that an IFsubmodule Aof Mis center in IFgraph of Mif and only ifAis a center in crisp graph of M.In prime ring R, we show that every vertex of intersection graph of IFideals of Ris center. In general the nature of intersection graph of IFsubmodules of a module under intersection, homomorphic images, finite sum and other algebraic operations of its vertices, are investigated.