Journal of Applied and Pure Mathematics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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SOME RESULTS ON CENTRALIZERS OF SEMIPRIME RINGS

  • ANSARI, ABU ZAID (Department of Mathematics, Faculty of Science, Islamic University of Madinah)
  • Received : 2021.11.18
  • Accepted : 2022.04.20
  • Published : 2022.07.30
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Abstract

The objective of this research paper is to prove that an additive mapping T from a semiprime ring R to itself will be centralizer having a suitable torsion restriction on R if it satisfy any one of the following algebraic equations (a) 2T(xnynxn) = T(xn)ynxn + xnynT(xn) (b) 3T(xnynxn) = T(xn)ynxn+xnT(yn)xn+xnynT(xn) for every x, y ∈ R. Further, few extensions of these results are also presented in the framework of *-ring.

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References

  1. M. Ashraf and M.R. Mozumder On Jordan α-*-Centralizers in Semiprime Rings with Involution, International Journal of Mathematics and Mathematical Sciences 7 (2012), 1103-1112.
  2. K.I. Beidar, W.S. Mattindale and A.V. Mikhalev, Ring with generalized identities, Markel Dekker Inc., New York, 1996.
  3. S. Helgosen, Multipliers of Banach algebras, Annals of Mathematics 64 (1956), 240-254. https://doi.org/10.2307/1969971
  4. I.N. Herstein, Topics in ring theory, The University of Chicago Press, Chicago, 1969.
  5. B.E. Johnson, An introduction to the theory of centralizers, Proceedings of the London Mathematical Society 14 (1964), 299-320. https://doi.org/10.1112/plms/s3-14.2.299
  6. B.E. Johnson, Centralizers on certain topological algebras, Journal of the London Mathematical Society 39 (1964), 603-614. https://doi.org/10.1112/jlms/s1-39.1.603
  7. B.E. Johnson, Continuity of centralizers on Banach algebras, Journal of the London Mathematical Society 41 (1966), 639-640. https://doi.org/10.1112/jlms/s1-41.1.639
  8. J. Vukman, An identity related to centralizers in semiprime rings, Commentationes Mathematicae Universitatis Carolinae 40 (1999), 447-456.
  9. J. Vukman and I. Kosi-Ulbl, An equation related to centralizers in semiprime rings, Glasnik Matematicki 38 (2003), 253-261. https://doi.org/10.3336/gm.38.2.04
  10. J.K. Wang, Multipliers of commutative Banach algebras, Pacific Journal of Mathematics 11 (1961), 1131-1149. https://doi.org/10.2140/pjm.1961.11.1131
  11. J.G. Wendel, Left centralizers and isomorphisms of group algebras, Pacific Journal of Mathematics 2 (1952), 251-266. https://doi.org/10.2140/pjm.1952.2.251
  12. B. Zalar, On centralizers of semiprime rings, Commentationes Mathematicae Universitatis Carolinae 32 (1991), 609-614.