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Identities with Skew Derivations

✍ Scribed by Chen-Lian Chuang

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
313 KB
Volume
224
Category
Article
ISSN
0021-8693

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✦ Synopsis

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 compositions of skew derivations, then R also satisfies a generalized polynomial identity (without skew derivations). We actually work in a more general context, in which higher (skew) derivations in the literature known to the author are all covered.

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If Οƒ is an automorphism and Ξ΄ is a q-skew Οƒ-derivation of a ring R, then the subring of invariants is the set R Ξ΄ = r ∈ R Ξ΄ r = 0 . The main result of this paper is Theorem. Let R be a prime algebra with a q-skew Οƒ-derivation Ξ΄, where Ξ΄ and Οƒ are algebraic. If R Ξ΄ satisfies a P. I., then R satisfies