Georgian Mathematical Journal

, Volume 3, Issue 1, pp 1–10 | Cite as

Commutativity for a certain class of rings

  • Hamza A. S. Abujabal


We discuss the commutativity of certain rings with unity 1 and one-sideds-unital rings under each of the following conditions:x r [x s ,y]=±[x,y t ]x n x r [x s ,y]=±x n [x,y t ]x r [x s ,y]=±[x,y t ]y m , andx r [x s ,y]=±y m [x,y t ], wherer, n, andm are non-negative integers andt>1,s are positive integers such that eithers, t are relatively prime ors[x,y]=0 implies [x,y]=0. Further, we improve the result of [6, Theorem 3] and reprove several recent results.

1991 Mathematics Subject Classification


Key words and phrases

Commutativity of rings ring with unity s-unital rings 


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  1. 1.
    H. A. S. Abujabal and V. Perić, Commutativity ofs-unital rings through a Streb result.Radovi Mat. 7 (1991), 73–92.Google Scholar
  2. 2.
    H. Komatsu, A commutativity theorem for rings.Math. J. Okayama Univ. 26 (1984), 109–111.Google Scholar
  3. 3.
    M. A. Quadri and M. A. Khan, A commutativity theorem for associative rings.Math. Japonica 33 (1988), 275–279.Google Scholar
  4. 4.
    H. G. Moore, Generalizedn-like rings and commutativity.Canad. Math. Bull. 23 (1980), 449–452.Google Scholar
  5. 6.
    N. Jacobson, Structure of rings.Amer. Math. Soc., Colloq. Publ., 1964.Google Scholar
  6. 7.
    W. K. Nicholson and A. Yaqub, Commutativity theorems for rings and groups.Canad. Math. Bull. 22 (1979), 419–423.Google Scholar
  7. 8.
    T. P. Kezlan, A note on commutativity of semi-prime PI rings.Math. Japonica 27 (1982), 267–268.Google Scholar
  8. 9.
    T. P. Kezlan, On identities which are equivalent with commutativity.Math. Japonica 29 (1984), 135–139.Google Scholar
  9. 10.
    H. E. Bell, M. A. Quadri, and M. Ashraf Commutativity of rings with some commutator constraints.Radovi Mat. 5 (1989), 223–230.Google Scholar
  10. 11.
    T. P. Kezlan, On commutativity theorems for PI ring with unity.Tamkang J. Math. 24 (1993), 29–36.Google Scholar
  11. 12.
    H. E. Bell, M. A. Quadri, and M. A. Khan, Two commutativity theorems for rings.Radovi Mat. 3 (1987), 255–260.Google Scholar
  12. 13.
    Y. Hirano, Y. Kobayashi, and H. Tominaga, Some polynomial identities and commutativity ofs-unital rings.Math. J. Okayama Univ. 24 (1982), 7–13.Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Hamza A. S. Abujabal
    • 1
  1. 1.Department of MathematicsKing Abdul Aziz UniversityJeddahSaudi Arabia

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