Loading...

Some results on the intersection graphs of ideals of rings

Akbari, S ; Sharif University of Technology | 2013

202 Viewed
  1. Type of Document: Article
  2. DOI: 10.1142/S0219498812501988
  3. Publisher: 2013
  4. Abstract:
  5. Let R be a ring with unity and I(R)* be the set of all nontrivial left ideals of R. The intersection graph of ideals of R, denoted by G(R), is a graph with the vertex set I(R)* and two distinct vertices I and J are adjacent if and only if I ∩ J ≠ 0. In this paper, we study some connections between the graph-theoretic properties of this graph and some algebraic properties of rings. We characterize all rings whose intersection graphs of ideals are not connected. Also we determine all rings whose clique number of the intersection graphs of ideals is finite. Among other results, it is shown that for a ring R, if the clique number of G(R) is finite, then the chromatic number is finite and if R is a reduced ring, then both are equal
  6. Keywords:
  7. Chromatic number ; Clique number ; Intersection graph of ideals of a ring
  8. Source: Journal of Algebra and its Applications ; Volume 12, Issue 4 , 2013 ; 02194988 (ISSN)
  9. URL: http://www.tandfonline.com/doi/abs/10.1080/03081087.2013.769101