Generalized Derivations with Periodic Values
Keyword(s):
Let R be a prime ring and n > 1 be a fixed positive integer. If g is a nonzero generalized derivation of R such that g(x)n=g(x) for all x ∈ R, then R is commutative except when R is a subring of the 2 × 2 matrix ring over a field. Moreover, we generalize the result to the case g(f(xi))n = g(f(xi)) for all x1, x2, …, xt∈ R, where f(Xi) is a multilinear polynomial.
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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2018 ◽
Vol 17
(03)
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pp. 1850046
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Keyword(s):
2015 ◽
Vol 34
(2)
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pp. 29
Keyword(s):