Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900873 | Applied Mathematics and Computation | 2018 | 6 Pages |
Abstract
For a ring R (not necessarily commutative) with identity, the comaximal right ideal graph of R, denoted by G(R), is a graph whose vertices are the nonzero proper right ideals of R, and two distinct vertices I and J are adjacent if and only if I+J=R. In this paper we consider a subgraph G*(R) of G(R) induced by V(G(R))âJ(R), where J(R) is the set of all proper right ideals contained in the Jacobson radical of R. We prove that if R contains a nontrivial central idempotent, then G*(R) is a star graph if and only if R is isomorphic to the direct product of two local rings, and one of these two rings has unique maximal right ideal {0}. In addition, we also show that R has at least two maximal right ideals if and only if G*(R) is connected and its diameter is at most 3, then completely characterize the diameter of this graph.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Shouqiang Shen, Weijun Liu, Lihua Feng,