대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제27권1호
  • /
  • Pages.69-76
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  • 2012
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ON LEFT α-MULTIPLIERS AND COMMUTATIVITY OF SEMIPRIME RINGS

  • Ali, Shakir (Department of Mathematics Aligarh Muslim University) ;
  • Huang, Shuliang (Department of Mathematics Chuzhou University)
  • 투고 : 2010.10.13
  • 발행 : 2012.01.31
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초록

Let R be a ring, and ${\alpha}$ be an endomorphism of R. An additive mapping H : R ${\rightarrow}$ R is called a left ${\alpha}$-multiplier (centralizer) if H(xy) = H(x)${\alpha}$(y) holds for all x,y $\in$ R. In this paper, we shall investigate the commutativity of prime and semiprime rings admitting left ${\alpha}$-multiplier satisfying any one of the properties: (i) H([x,y])-[x,y] = 0, (ii) H([x,y])+[x,y] = 0, (iii) $H(x{\circ}y)-x{\circ}y=0$, (iv) $H(x{\circ}y)+x{\circ}y=0$, (v) H(xy) = xy, (vi) H(xy) = yx, (vii) $H(x^2)=x^2$, (viii) $H(x^2)=-x^2$ for all x, y in some appropriate subset of R.

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참고문헌

  1. E. Albash, On $\tau$-centralizers of semiprime rings, Siberian Math. J. 48 (2007), no. 2, 191-196. https://doi.org/10.1007/s11202-007-0021-5
  2. S. Ali and C. Haetinger, Jordan $\alpha$-centralizers in rings and some applications, Bol. Soc. Paran. Math. (3) 26 (2008), no. 1-2, 71-80.
  3. F. W. Anderson, Lectures on noncommutative rings, Univ. of Oregon, 2002.
  4. M. Ashraf and S. Ali, On left multipliers and the commutativity of prime rings, Demonstratio Math. 41 (2008), no. 4, 763-771.
  5. M. Ashraf, S. Ali, and C. Haetinger, On derivations in rings and their applications, Aligarh Bull. Math. 25 (2006), no. 2, 79-107.
  6. M. Bresar, On the distance of the composition of two derivations to the generalized derivations, Glasgow Math. J. 33 (1991), no. 1, 89-93. https://doi.org/10.1017/S0017089500008077
  7. W. Cortes and C. Haetinger, On Lie ideals and left Jordan $\alpha$-centralizers of 2-torsion-free rings, Math. J. Okayama Univ. 51 (2009), 111-119.
  8. M. N. Daif and M. S. Tammam EL-Sayiad, On $\alpha$-centralizers of semiprime rings (II), St. Petersburg Math. J. 21 (2010), no. 1, 43-52. https://doi.org/10.1090/S1061-0022-09-01084-X
  9. I. N. Herstein, Rings with Involution, University of Chicago Press, Chicago 1976.
  10. M. A. Quadri, M. S. Khan, and N. Rehman, Generalized derivations and commutativity of prime rings, Indian J. Pure Appl. Math. 34 (2003), no. 9, 1393-1396.
  11. J. Vukman and I. Kosi-Ulbl, On centralizers of semiprime rings, Aequationes Math. 66 (2003), no. 3, 277-283. https://doi.org/10.1007/s00010-003-2681-y
  12. J. Vukman and I. Kosi-Ulbl, On centralizers of semiprime rings with involution, Studia Sci. Math. Hungar. 43 (2006), no. 1, 61-67.
  13. B. Zalar, On centralizers of semiprime rings, Comment. Math. Univ. Carolin. 32(1991), no. 4, 609-614.

피인용 문헌

  1. Generalized Derivations on Power Values of Lie Ideals in Prime and Semiprime Rings vol.2014, 2014, https://doi.org/10.1155/2014/216039