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On commuting graphs of semisimple rings

Akbari, S ; Sharif University of Technology | 2004

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  1. Type of Document: Article
  2. DOI: 10.1016/j.laa.2004.05.001
  3. Publisher: 2004
  4. Abstract:
  5. Let R be a non-commutative ring. The commuting graph of R denoted by Λ (R), is a graph with vertex set R Z(R), and two distinct vertices a and b are adjacent if ab = ba. In this paper we investigate some properties of Λ(R), whenever R is a finite semisimple ring. For any finite field F, we obtain minimum degree, maximum degree and clique number of Λ(M n (F)). Also it is shown that for any two finite semisimple rings R and S, if Λ(R) ≃ Λ(S), then there are commutative semisimple rings R1 and S1 and semisimple ring T such that R ≃T × R1, S ≃ T × S1 and |R1| = |S1|. © 2004 Elsevier Inc. All rights reserved
  6. Keywords:
  7. Commuting graph ; Semisimple ring
  8. Source: Linear Algebra and Its Applications ; Volume 390, Issue 1-3 , 2004 , Pages 345-355 ; 00243795 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0024379504002393