Lee, Tsiu-Kwen; Liu, Kun-Shan Generalized skew derivations with algebraic values of bounded degree. (English) Zbl 1285.16038 Houston J. Math. 39, No. 3, 733-740 (2013). 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. Reviewer: Ajda Fošner (Koper) Cited in 9 Documents 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 Keywords:automorphisms; prime rings; generalized skew derivations; GPI; prime algebras; derivations with algebraic values; primitive rings PDFBibTeX XMLCite \textit{T.-K. Lee} and \textit{K.-S. Liu}, Houston J. Math. 39, No. 3, 733--740 (2013; Zbl 1285.16038)