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Some results on the intersection graph of ideals of matrix algebras

Akbari, S ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1080/03081087.2013.769101
  3. Abstract:
  4. Let be a ring and be the set of all non-trivial left ideals of. The intersection graph of ideals of, denoted by, is a graph with the vertex set and two distinct vertices and are adjacent if and only if. In this paper, we classify all rings (not necessarily commutative) whose domination number of the intersection graph of ideals is at least 2. Moreover, some results on the intersection graphs of ideals of matrix algebras over a finite field are given. For instance, we determine the domination number, the clique number and the independence number of. We prove that if is a positive integer and, then the domination number of is. Among other results, we show that if, where is a positive integer and is a ring, then. Also, it is proved that if and are two finite reduced rings and, for some positive integers, then and
  5. Keywords:
  6. Intersecting family of subspaces ; Intersection graph of ideals of a ring ; Matrix algebra
  7. Source: Linear and Multilinear Algebra ; Volume 62, Issue 2 , February , 2014 , Pages 195-206 ; ISSN: 03081087
  8. URL: http://www.tandfonline.com/doi/abs/10.1080/03081087.2013.769101#.VdBncH01rcs