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Generalized Lie derivations on skew elements of prime algebras with involution

✍ Scribed by Pao-Kuei Liau; Cheng-Kai Liu

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
222 KB
Volume
435
Category
Article
ISSN
0024-3795

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✦ Synopsis

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.

πŸ“œ SIMILAR VOLUMES

Lie Derivations of the Skew Elements of
Lie Derivations of the Skew Elements of Prime Rings with Involution
✍ Gordon A. Swain πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 258 KB

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 Ε½ . R . Assume that RC : C / 1, 4, 16. It is shown that any Lie derivation of K into Β² : itself can be extended to an ordinary derivation

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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 de