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On generalized Lie derivations of Lie ideals of prime algebras

✍ Scribed by Ping-Bao Liao; Cheng-Kai Liu

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
136 KB
Volume
430
Category
Article
ISSN
0024-3795

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✦ Synopsis

Let A be a prime algebra of characteristic not 2 with extended centroid C, let R be a noncentral Lie ideal of A and let B be the subalgebra of A generated by R. If f , d : R β†’ A are linear maps satisfying that f ([x, y]) = f (x)yf (y)x + xd(y)yd(x) for all x, y ∈ R, then there exist a generalized derivation g : B β†’ AC + C and a linear map ΞΆ : R β†’ C such that f (x) = g(x) + ΞΆ(x) for all x ∈ R and ΞΆ([R, R]) = 0 provided that A does not satisfy the standard identity of degree 18.

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