Some bounds for commuting probability of finite rings

  • Dhiren Kumar BasnetEmail author
  • Jutirekha Dutta


Let R be a finite ring. The commuting probability of R is the probability that any two randomly chosen elements of R commute. In this paper, we obtain some bounds for commuting the probability of R.


Finite ring commuting probability 

2010 Mathematics Subject Classification

16U70 16U80 



The authors would like to thank the referee for his/her useful comments.


  1. 1.
    Buckley S M and Machale D, Contrasting the commuting probabilities of groups and rings, preprintGoogle Scholar
  2. 2.
    Buckley S M, Machale D and N\(\acute{{\rm i}}\) Sh\(\acute{{\rm e}}\) A, Finite rings with many commuting pairs of elements, preprintGoogle Scholar
  3. 3.
    Das A K, Nath R K and Pournaki M R, A survey on the estimation of commutativity in finite groups, Southeast Asian Bull. Math. 37 (2013) 161–180MathSciNetzbMATHGoogle Scholar
  4. 4.
    Erdös P and Turán P, On some problems of a statistical group-theory IV, Acta. Math. Acad. Sci. Hungar. 19 (1968) 413–435MathSciNetCrossRefGoogle Scholar
  5. 5.
    MacHale D, Commutativity in finite rings, Amer. Math. Monthly 83 (1976) 30–32MathSciNetCrossRefGoogle Scholar
  6. 6.
    Nath R K and Das A K, On a lower bound of commutativity degree, Rend. Circ. Mat. Palermo 59 (2010) 137–142MathSciNetCrossRefGoogle Scholar
  7. 7.
    Nath R K and Yadav M K, Some results on relative commutativity degree, Rend. Circ. Mat. Palermo 64(2) (2015) 229–239MathSciNetCrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTezpur UniversityNapaamIndia

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