Remarks on Certain Identities with Derivations on Semiprime Rings


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Fosner A., Baydar N. , STRASEK R.

UKRAINIAN MATHEMATICAL JOURNAL, cilt.66, ss.1609-1614, 2015 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 66 Konu: 10
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1007/s11253-015-1037-9
  • Dergi Adı: UKRAINIAN MATHEMATICAL JOURNAL
  • Sayfa Sayıları: ss.1609-1614

Özet

Let n be a fixed positive integer, let R be a (2n)! -torsion-free semiprime ring, let be an automorphism or an anti-automorphism of R, and let D (1) , D (2) : R -> R be derivations. We prove the following result: If (D (1) (2) (x) + D (2)(x)) (n) a similar to aEuro parts per thousand alpha(x) (n) = 0 holds for all x a R, then D (1) = D (2) = 0. The same is true if R is a 2-torsion free semiprime ring and F(x) A degrees beta(x) = 0 for all x a R, where F(x) = (D (1) (2) (x) + D (2)(x)) a similar to aEuro parts per thousand alpha(x), x aaEuro parts per thousand R, and beta is any automorphism or antiautomorphism on R.