대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제34권4호
  • /
  • Pages.1099-1104
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  • 2019
  • /
  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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CENTRALIZING AND COMMUTING INVOLUTION IN RINGS WITH DERIVATIONS

  • Khan, Abdul Nadim (Department of Mathematics Faculty of Science & Arts-Rabigh King Abdulaziz University)
  • 투고 : 2018.09.19
  • 심사 : 2018.12.27
  • 발행 : 2019.10.31
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초록

In [1], Ali and Dar proved the ${\ast}$-version of classical theorem due to Posner [15, Theorem] with involution of the second kind. The main objective of this paper is to improve the above mentioned result without the condition of the second kind involution. Moreover, a related result has been discussed.

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참고문헌

  1. S. Ali and N. A. Dar, On *-centralizing mappings in rings with involution, Georgian Math. J. 21 (2014), no. 1, 25-28. https://doi.org/10.1515/gmj-2014-0006
  2. S. Ali and N. A. Dar, On centralizers of prime rings with involution, Bull. Iranian Math. Soc. 41 (2015), no. 6, 1465-1475.
  3. S. Ali, N. A. Dar, and M. Asci, On derivations and commutativity of prime rings with involution, Georgian Math. J. 23 (2016), no. 1, 9-14. https://doi.org/10.1515/gmj-2015-0016
  4. S. Ali, A. N. Khan, and N. A. Dar, Herstein's theorem for generalized derivations in rings with involution, Hacet. J. Math. Stat. 46 (2017), no. 6, 1029-1034.
  5. R. Awtar, Lie ideals and commuting mappings in prime rings, Publ. Math. Debrecen 43 (1993), no. 1-2, 169-180.
  6. M. Bresar, Centralizing mappings and derivations in prime rings, J. Algebra 156 (1993), no. 2, 385-394. https://doi.org/10.1006/jabr.1993.1080
  7. M. Bresar, Commuting maps: a survey, Taiwanese J. Math. 8 (2004), no. 3, 361-397. https://doi.org/10.11650/twjm/1500407660
  8. N. A. Dar and S. Ali, On *-commuting mappings and derivations in rings with involution, Turkish J. Math. 40 (2016), no. 4, 884-894. https://doi.org/10.3906/mat-1508-61
  9. N. A. Dar and A. N. Khan, Generalized derivations in rings with involution, Algebra Colloq. 24 (2017), no. 3, 393-399. https://doi.org/10.1142/S1005386717000244
  10. N. J. Divinsky, On commuting automorphisms of rings, Trans. Roy. Soc. Canada. Sect. III. (3) 49 (1955), 19-22.
  11. I. N. Herstein, Rings with Involution, The University of Chicago Press, Chicago, IL, 1976.
  12. P. H. Lee and T. K. Lee, Derivations centralizing symmetric or skew elements, Bull. Inst. Math. Acad. Sinica 14 (1986), no. 3, 249-256.
  13. A. Mamouni, B. Nejjar, and L. Oukhtite, Differential identities on prime rings with involution, J. Algebra Appl. 17 (2018), no. 9, 1850163, 11 pp. https://doi.org/10.1142/S0219498818501633
  14. B. Nejjar, A. Kacha, A. Mamouni, and L. Oukhtie, Commutativity theorems in rings with involution, Comm. Algebra 45 (2017), no. 2, 698-708. https://doi.org/10.1080/00927872.2016.1172629
  15. E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1100. https://doi.org/10.2307/2032686
  16. J. Vukman, Commuting and centralizing mappings in prime rings, Proc. Amer. Math. Soc. 109 (1990), no. 1, 47-52. https://doi.org/10.2307/2048360