Generalized derivations in prime rings

Vishal; Reetu; Anju

doi:https://doi.org/10.14445/22315373/IJMTT-V46P506

International Journal of Mathematics Trends and Technology

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Volume 46 | Number 1 | Year 2017 | Article Id. IJMTT-V46P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V46P506

Generalized derivations in prime rings

Vishal, Reetu, Anju

Abstract

Let R be a prime ring and I be a non zero ideal of R: Suppose that F; G;H : R ! R are generalized derivations associated with derivations d; g; h respectively. If the following holds (i)F(xy)+G(x)H(y)+[(x); y] = 0; for all x; y 2 I; where is any map on R; then R is commutative.

Keywords

Prime ring, Ideal, Commuting map, Generalized derivation.

References

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Citation :

Vishal, Reetu, Anju, "Generalized derivations in prime rings," International Journal of Mathematics Trends and Technology (IJMTT), vol. 46, no. 1, pp. 29-33, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V46P506