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The clique numbers of regular graphs of matrix algebras are finite

Akbari, S ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. DOI: 10.1016/j.laa.2009.06.005
  3. Publisher: 2009
  4. Abstract:
  5. Let F be a field, char (F) ≠ 2, and S ⊆ GLn (F), where n is a positive integer. In this paper we show that if for every distinct elements x, y ∈ S, x + y is singular, then S is finite. We conjecture that this result is true if one replaces field with a division ring. © 2009 Elsevier Inc. All rights reserved
  6. Keywords:
  7. Clique number ; Matrix algebra ; Regular graph ; Clique number ; Distinct elements ; Positive integers ; Regular graph ; Regular graphs ; Algebra ; Graph theory ; Matrix algebra
  8. Source: Linear Algebra and Its Applications ; Volume 431, Issue 10 , 2009 , Pages 1715-1718 ; 00243795 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0024379509003036