Table of Contents
International Scholarly Research Notices
Volume 2014 (2014), Article ID 563284, 9 pages
http://dx.doi.org/10.1155/2014/563284
Research Article

Two-Sided Annihilator Condition with Generalized Derivations on Multilinear Polynomials

Department of Mathematics, Faculty of Sciences, University of Messina, Via F. Stagno D’Alcontres 31, 98166 Messina, Italy

Received 30 April 2014; Accepted 15 July 2014; Published 28 October 2014

Academic Editor: Ali Jaballah

Copyright © 2014 V. De Filippis et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. K. I. Beidar, W. S. Martindale III, and A. V. Mikhalev, Rings with Generalized Identities, Pure and Applied Mathematics, Dekker, New York, NY, USA, 1996.
  2. J. Lambek, Lectures on Rings and Modules, Blaisdell Publishing, Waltham, Mass, USA, 1966. View at MathSciNet
  3. C. Faith, Lectures on Injective Modules and Quotient Rings, Lecture Notes in Mathematics, Springer, New York, NY, USA, 1967. View at MathSciNet
  4. E. C. Posner, “Derivations in prime rings,” Proceedings of the American Mathematical Society, vol. 8, pp. 1093–1100, 1957. View at Publisher · View at Google Scholar · View at MathSciNet
  5. C. Lanski, “An Engel condition with derivation,” Proceedings of the American Mathematical Society, vol. 118, no. 3, pp. 731–734, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. P. H. Lee and T. K. Lee, “Derivations with Engel conditions on multilinear polynomials,” Proceedings of the American Mathematical Society, vol. 124, no. 9, pp. 2625–2629, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. V. de Filippis and O. M. di Vincenzo, “Posner's second theorem and an annihilator condition,” Mathematica Pannonica, vol. 12, no. 1, pp. 69–81, 2001. View at Google Scholar · View at MathSciNet
  8. C. K. Liu, “Derivations with Engel and annihilator conditions on multilinear polynomials,” Communications in Algebra, vol. 33, no. 3, pp. 719–725, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. Y. Wang, “Annihilator conditions of derivations on multilinear polynomials,” Communications in Algebra, vol. 39, no. 1, pp. 237–246, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  10. V. de Filippis, “Posner's second theorem and an annihilator condition with generalized derivations,” Turkish Journal of Mathematics, vol. 32, no. 2, pp. 197–211, 2008. View at Google Scholar · View at MathSciNet · View at Scopus
  11. T. K. Lee, “Generalized derivations of left faithful rings,” Communications in Algebra, vol. 27, no. 8, pp. 4057–4073, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. C. Chuang, “GPIs having coefficients in Utumi quotient rings,” Proceedings of the American Mathematical Society, vol. 103, no. 3, pp. 723–728, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  13. V. de Filippis and O. M. Di Vincenzo, “Vanishing derivations and centralizers of generalized derivations on multilinear polynomials,” Communications in Algebra, vol. 40, no. 6, pp. 1918–1932, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. W. S. Martindale III, “Prime rings satisfying a generalized polynomial identity,” Journal of Algebra, vol. 12, no. 4, pp. 576–584, 1969. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. U. Leron, “Nil and power-central polynomials in rings,” Transactions of the American Mathematical Society, vol. 202, pp. 97–103, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. T. K. Lee, “Semiprime rings with differential identities,” Bulletin of the Institute of Mathematics. Academia Sinica, vol. 20, no. 1, pp. 27–38, 1992. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. C. Chuang, “The additive subgroup generated by a polynomial,” Israel Journal of Mathematics, vol. 59, no. 1, pp. 98–106, 1987. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. K. I. Beidar, “Rings with generalized identities,” Moscow University Mathematics Bulletin, vol. 33, pp. 53–58, 1978. View at Google Scholar
  19. T. S. Erickson, W. S. Martindale III, and J. M. Osborn, “Prime nonassociative algebras,” Pacific Journal of Mathematics, vol. 60, no. 1, pp. 49–63, 1975. View at Publisher · View at Google Scholar · View at MathSciNet
  20. N. Jacobson, Structure of Rings, American Mathematical Society, Providence, RI, USA, 1964.
  21. T. L. Wong, “Derivations with power-central values on multilinear polynomials,” Algebra Colloquium, vol. 3, no. 4, pp. 369–378, 1996. View at Google Scholar · View at MathSciNet
  22. V. K. Kharchenko, “Differential identities of prime rings,” Algebra and Logic, vol. 17, no. 2, pp. 155–168, 1978. View at Google Scholar · View at MathSciNet