Let be a prime ring, the right Martindale quotient ring of and the extended centroid of .
In this paper, we discuss the relationship between the structure of prime rings and the behavior of skew derivations on multilinear polynomials. More precisely, we investigate the m-potent commutators of skew derivations involving multilinear polynomials, i.e.,
where , is a non-central multilinear polynomial over and δ is a skew derivation of .
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Proc. Indian Acad. Sci. Math. Sci. 127 (2017), no. 1, 91–98.
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Vanishing derivations and centralizers of generalized derivations on multilinear polynomials,
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V. De Filippis and G. Scudo,
Strong commutativity and Engel condition preserving maps in prime and semiprime rings,
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N. Rehman and M. Arif Raza,
On m-commuting mappings with skew derivations in prime rings (in Russian),
Algebra i Analiz 27 (2015), no. 4, 74–86;
translation in St. Petersburg Math. J. 27 (2016), no. 4, 641–650.
L. H. Rowen,
Polynomial Identities in Ring Theory,
Pure Appl. Math.84,
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Power-centralizing automorphisms of Lie ideals in prime rings,
Comm. Algebra 34 (2006), no. 2, 609–615.
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