Symmetric skew 4-derivations on prime rings

Faiza Shujat, Abu Zaid Ansari

Abstract


For a ring R with an automorphism α a 4-additive mapping D : R4−→ R is called a skew 4-derivation w.r.t. α if it is a α-derivation of R for each argument. Namely it is always an α-derivation of R for the argument being left once (3) arguments are fixed by (3) elements in R. In the present note, begin with a result of Jung and Park [5], we prove that if a skew 4-derivation D associated with an automorphism α with trace f of a noncommutative prime ring R under suitable torsion condition satisfying [f(x),α(x)] = 0 for all x ∈ I, a nonzero ideal of R, then D = 0.

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How to Cite this Article:

Faiza Shujat, Abu Zaid Ansari, Symmetric skew 4-derivations on prime rings, Journal of Mathematical and Computational Science, Vol 4, No 4 (2014), 649-656

Copyright © 2014 Faiza Shujat, Abu Zaid Ansari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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