Research ArticleOpen accessIn the keywordsA Kind of Intersection Graphs on Ideals of a RingA. A. TalebiProblem statement: Let R be a ring. The graph G(R) is the graph whose vertices are nontrivial ideal of R and in which two vertices u, v are joined by an edge, if and only if u ∩ v #{0}. Approach: In this study we study some properties of G(R). Results: We obtain conditions of R such that G(R) is … …Journal of Mathematics and Statistics, Vol. 8, Issue 1 · 6 Feb 2012 · 7,258 accessesView PDFCite
Research ArticleOpen accessIn the abstractOn Containment and Radical Graphs of a Commutative RingSaba Al-KaseasbehIn this study, we consider various graphs with the vertices being sets of ideals of a commutative ring with identity, R. How we define the edge set will vary according to distinct ideal theoretic properties. We apply a graphical approach to the study of ideal relationships in commutative rings and from this we obtain some properties of their graphs. …Journal of Mathematics and Statistics, Vol. 12, Issue 4 · 29 Dec 2016 · 7,266 accessesView PDFCite