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Nonlinear strong commutativity preserving maps on skew elements of prime rings with involution

✍ Scribed by Pao-Kuei Liau; Wei-Lu Huang; Cheng-Kai Liu

Book ID: 113772150
Publisher: Elsevier Science
Year: 2012
Tongue: English
Weight: 304 KB
Volume: 436
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2011.10.014

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Let R be a prime ring with involution of the first kind, and characteristic / 2, 3. Let K denote the skew elements of R, and let C denote the extended centroid of Ž . R . Assume that RC : C / 1, 4, 16. It is shown that any Lie derivation of K into ² : itself can be extended to an ordinary derivation

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We characterize generalized Lie derivations on skew elements of prime algebras A with involution, provided that A does not satisfy polynomial identities of low degree. The analogous result for matrix algebras is also described.