A result concerning nilpotent values with generalized skew derivations on Lie ideals

Let n≥1 be a fixed integer, R a prime ring with its right Martindale quotient ring Q, C the extended centroid, and L a non-central Lie ideal of R. If F is a generalized skew derivation of R such that (F(x)F(y)−yx) n  = 0 for all x,y∈L, then char(R) = 2 and R⊆M 2 (C), the ring of 2×2 matrices over C....

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Bibliographic Details
Published in:Communications in algebra 2018-12, Vol.46 (12), p.5330-5341
Main Authors: Sharma, R. K., Dhara, B., Filippis, V. De, Garg, C.
Format: Article
Language:English
Subjects:
Automorphism
generalized skew derivation
Lie ideal
prime ring
right Martindale quotient ring
Rings (mathematics)
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Summary:Let n≥1 be a fixed integer, R a prime ring with its right Martindale quotient ring Q, C the extended centroid, and L a non-central Lie ideal of R. If F is a generalized skew derivation of R such that (F(x)F(y)−yx) n  = 0 for all x,y∈L, then char(R) = 2 and R⊆M 2 (C), the ring of 2×2 matrices over C.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2018.1464170