When Is the Complement of the Comaximal Graph of a Commutative Ring Planar?. (6th April 2014)

• Record Type: Journal Article
• Authors: Visweswaran, S.; Parejiya, Jaydeep
• Other Names: Anderson D. F. Academic Editor.; Bakalov B. Academic Editor.; Zimmermann A. Academic Editor.
• Is Part Of: ISRN algebra. Volume 2014(2014)
• Publication Date: 2014-04-06
• Subjects: Algebra -- Periodicals; Algebra; Periodicals; Electronic journals; 512
• DOI: 10.1155/2014/736043
• Languages: English
• ISSNs: 2090-6285

Abstract

Abstract : LetR be a commutative ring with identity. In this paper we classify ringsR such that the complement of comaximal graph ofR is planar. We also consider the subgraph of the complement of comaximal graph ofR induced on the setS of all nonunits ofR with the property that each element ofS is not in the Jacobson radical ofR and classify ringsR such that this subgraph is planar.