Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

DERIVATIONS ON PRIME AND SEMI-PRIME RINGS

  • Published : 2002.08.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we will show that if there exist derivations D, G on a n!-torsion free semi-prime ring R such that the mapping $D^2+G$ is n-commuting on R, then D and G are both commuting on R. And we shall give the algebraic conditions on a ring that a Jordan derivation is zero.

Keywords

References

  1. Proc. Amer. Math. v.104 jordan derivations on semiprime rings M. $Bre\~{s}ar$/ https://doi.org/10.1090/S0002-9939-1988-0929422-1
  2. Rad. Math. v.5 Orthogonal derivation and an extension of a Theorem of Posner M. $Bre\~{s}ar$/;J. Vukman
  3. Canad. Math. Bull. v.24 no.4 Semiprime rings with nilpotent derivatives L. O. Chung;J. Luh https://doi.org/10.4153/CMB-1981-064-9
  4. Communications in algebras v.23 no.10 On derivations and commutativity in semiprime rings Q. Deng;H. E. Bell https://doi.org/10.1080/00927879508825427
  5. Amer. J. Math. v.90 Continuity of derivations and a problem of kaplansky B. E. Johnson;A. M. Sinclair https://doi.org/10.2307/2373290
  6. Korean J. Comput. & Appl. Math.(series A) v.7 Jordan derivations on noncommutative Banach algebras K. H. Park;B. D. Kim
  7. Proc. Amer. Math. Soc. v.8 Derivations in prime rings E. Posner https://doi.org/10.1090/S0002-9939-1957-0095863-0
  8. Proc. Amer. Math. Soc. v.24 Jordan homomorphism and derivations on semisiple Banach algebras A. M. Sinclair
  9. Glas. Mat. v.26 A result concerning derivations in noncommutative Banach algebras J. Vukman

Cited by

  1. Generalized Derivations and Commuting Additive Maps on Multilinear Polynomials in Prime Rings vol.68, pp.2, 2016, https://doi.org/10.1007/s11253-016-1219-0
  2. On n-commuting and n-skew-commuting maps with generalized derivations in prime and semiprime rings vol.52, pp.3, 2011, https://doi.org/10.1134/S0037446611030141