Journal of Mathematical Sciences

, Volume 207, Issue 5, pp 698–717 | Cite as

Graphs Defined by Orthogonality

  • B. R. Bakhadly
  • A. E. Guterman
  • O. V. Markova

The notion of graph generated by the mutual orthogonality relation for the elements of an associative ring is introduced. The main attention is paid to the commutative rings and to the matrix ring over a field and its various subrings and subsets. In particular, the diameters of the orthogonality graphs of the full matrix algebra over an arbitrary field and its subsets consisting of diagonal, diagonalizable, triangularizable, and nilpotent matrices are computed. Bibliography: 36 titles.


Local Ring Commutative Ring Zero Divisor Matrix Ring Minimal Prime Ideal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • B. R. Bakhadly
    • 1
  • A. E. Guterman
    • 1
  • O. V. Markova
    • 1
  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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