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Identities with Generalized Skew Derivations on Lie Ideals

✍ Scribed by Vincenzo De Filippis, Ajda Fošner, Feng Wei


Book ID
120965822
Publisher
Springer Netherlands
Year
2012
Tongue
English
Weight
384 KB
Volume
16
Category
Article
ISSN
1386-923X

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✍ Chen-Lian Chuang 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 313 KB

We solve affirmatively a problem, raised by Kharchenko, on identities with compositions of skew derivations: We define the notion of trivial identities with compositions of skew derivations, which is unique in a certain sense. It is proved that if a prime ring R satisfies a nontrivial identity with

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✍ Ping-Bao Liao; Cheng-Kai Liu 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 136 KB

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 → 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