Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON DERIVATIONS IN BANACH ALGEBRAS

  • Chang, Ick-Song (Department of Mathematics, Chungnam National University) ;
  • Jun, Kil-Woung (Department of Mathematics, Chungnam National University) ;
  • Jung, Yong-Soo (Department of Mathematics, Chungnam National University)
  • Published : 2002.11.01
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Abstract

Our main goal is to show that if there exist Jordan derivations D and G on a noncommutative (n + 1)!-torsion free prime ring R such that $$D(x)x^n-x^nG(x)\in\ C(R)$$ for all $x\in\ R$, then we have D=0 and G=0. We also prove that if there exists a derivation D on a noncommutative 2-torsion free prime ring R such that the mapping $\chi$longrightarrow[aD($\chi$), $\chi$] is commuting on R, then we have either a = 0 or D = 0.

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References

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Cited by

  1. Pairs of derivations on rings and Banach algebras vol.41, pp.2, 2008, https://doi.org/10.1515/dema-2013-0083
  2. Identities with Generalized Derivations on Prime Rings and Banach Algebras vol.19, pp.spec01, 2012, https://doi.org/10.1142/S1005386712000818
  3. Annihilator condition of a pair of derivations in prime and semiprime rings vol.47, pp.1, 2016, https://doi.org/10.1007/s13226-015-0166-z
  4. Skew Derivations of Prime Rings vol.47, pp.1, 2006, https://doi.org/10.1007/s11202-006-0016-7