Jacobson graph construction of ring Z3n, for n>1

Abstract

A group is called a ring if the group is a commutative under addition operation and satisfy the distributive and assosiative properties under multiplication operation. Suppose R is a commutative ring with non-zero identity, U is the unit of R, and J(R) is a Jacobson radical. Jacobson graph of a ring R denoted by image R is a graph with a vertex set is R\J(R) dan edge set is {(a, b)| 1-ab ∉ U}. The purpose of this research is to construct a Jacobson graph of ring Z 3n with n > 1. The results show that Jacobson graph of ring Z 3n is a disconected graph with two components.