Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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GENERALIZED DERIVATIONS ON PRIME RINGS SATISFYING CERTAIN IDENTITIES

  • Received : 2020.06.30
  • Accepted : 2020.11.17
  • Published : 2021.04.30
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Abstract

Let R be a ring with characteristic different from 2. An additive mapping F : R → R is called a generalized derivation on R if there exists a derivation d : R → R such that F(xy) = F(x)y + xd(y) holds for all x, y ∈ R. In the present paper, we show that if R is a prime ring satisfying certain identities involving a generalized derivation F associated with a derivation d, then R becomes commutative and in some cases d comes out to be zero (i.e., F becomes a left centralizer). We provide some counter examples to justify that the restrictions imposed in the hypotheses of our theorems are not superfluous.

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References

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