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Generalized skew derivations with algebraic values of bounded degree. (English) Zbl 1285.16038

Let \(g\colon R\to R\) be a nonzero generalized skew derivation on a prime ring \(R\) over the field \(F\). The authors show that if \(x^g\) is algebraic over \(F\) of bounded degree for all \(x\in R\), then \(R\) is primitive. Moreover, there exists a minimal idempotent \(e\in R\) such that \(eRe\) is a finite-dimensional central division algebra.

MSC:

16W25 Derivations, actions of Lie algebras
16N60 Prime and semiprime associative rings
16R50 Other kinds of identities (generalized polynomial, rational, involution)
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
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