Generalized skew-derivations annihilating and centralizing on multilinear polynomials in prime rings
\(f(x_1,\ldots ,x_n)^2 \) is central-valued on R;
R satisfies \(s_4\), the standered identity of degree 4.
KeywordsPrime ring derivation generalized derivation generalized skew derivation extended centroid
2010 Mathematics Subject Classification16N60 16W25 16R50
The authors would like to thank the referee for providing very helpful comments and suggestions. The authors are also grateful to the referee for providing a short proof of Lemma 3.6. The second author is supported by a grant from Science and Engineering Research Board (SERB), DST, New Delhi, India (Grant No. EMR/2016/004043 dated 29-Nov-2016).
- 2.Beidar K I, Martimdale III W S and Mikhalev A V, Rings with generalized identities, Pure and Applied Math. 196 (1996) (New York: Marcel Dekker)Google Scholar
- 15.Dhara B and Ali S, On \(n\)-centralizing generalized derivations in semiprime rings with applications to \(C^*\)-algebras, J. Algebra and its Applications 11(6) (2012) Paper No. 1250111, 11 pagesGoogle Scholar