Table of Contents
ISRN Algebra
Volume 2014, Article ID 736043, 8 pages
http://dx.doi.org/10.1155/2014/736043
Research Article

When Is the Complement of the Comaximal Graph of a Commutative Ring Planar?

Department of Mathematics, Saurashtra University, Rajkot 360 005, India

Received 10 February 2014; Accepted 6 March 2014; Published 6 April 2014

Academic Editors: D. F. Anderson, B. Bakalov, and A. Zimmermann

Copyright © 2014 S. Visweswaran and Jaydeep Parejiya. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be a commutative ring with identity. In this paper we classify rings such that the complement of comaximal graph of is planar. We also consider the subgraph of the complement of comaximal graph of induced on the set of all nonunits of with the property that each element of is not in the Jacobson radical of and classify rings such that this subgraph is planar.