Generalized Derivations Having the Same Power Values with Left Multiplications
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Let R be a prime ring with extended centroid C, maximal right ring of quotients U, a nonzero ideal I and a generalized derivation δ. Suppose δ(x)n =(ax)n for all x ∈ I, where a ∈ U and n is a fixed positive integer. Then δ(x)=λax for some λ ∈ C. We also prove two generalized versions by replacing I with a nonzero left ideal [Formula: see text] and a noncommutative Lie ideal L, respectively.
2018 ◽
Vol 11
(04)
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pp. 1850055
2012 ◽
Vol 11
(06)
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pp. 1250111
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2017 ◽
Vol 60
(4)
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pp. 721-735
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2010 ◽
Vol 17
(spec01)
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pp. 841-850
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2018 ◽
Vol 17
(03)
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pp. 1850046
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2015 ◽
Vol 34
(2)
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pp. 29
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