Correspondence Between Torsion and Annihilator Graph of Modules Zn Over Commutative Rings

Abstract

Let M be a module over a commutative ring. Torsion graph of module M is a simple undirected graph where the vertices are nonzero torsion elements of M and two different vertices x and y is adjacent if intersection of Ann(x) and Ann(y) is not zero. Meanwhile, the annihilator graph of the module M is a simple undirected graph where the vertex set is Z_R(M)\Ann_R(M) and two different vertices x and y is adjacent if union of Ann_M(x) and Ann_M(y) is not equal with Ann_M(xy). In this paper, we focus on the discussion of torsion graph and annihilator graph for integer modulo n module Zn. Moreover, we obtain some relation between them based on the prime factorization of n.