Bell, Howard E. On prime near-rings with generalized derivation. (English) Zbl 1152.16036 Int. J. Math. Math. Sci. 2008, Article ID 490316, 5 p. (2008). A generalized derivation \(f\) with associated derivation \(D\) in a (left) nearring \(N\) is an additive endomorphism of \(N\) such that \(f(xy)=f(x)y+xD(y)\), \(\forall x,y\in N\). Now \(3\)-prime \(2\)-torsion free nearrings with a generalized derivation fulfilling certain conditions are commutative rings. Reviewer: Celestina Cotti-Ferrero (Parma) Cited in 14 Documents MSC: 16Y30 Near-rings 16W25 Derivations, actions of Lie algebras 16U70 Center, normalizer (invariant elements) (associative rings and algebras) Keywords:prime nearrings; generalized derivations; commutativity theorems PDFBibTeX XMLCite \textit{H. E. Bell}, Int. J. Math. Math. Sci. 2008, Article ID 490316, 5 p. (2008; Zbl 1152.16036) Full Text: DOI EuDML References: [1] H. E. Bell and G. Mason, “On derivations in near-rings,” in Near-Rings and Near-Fields (Tübingen, 1985), G. Betsch, Ed., vol. 137 of North-Holland Mathematics Studies, pp. 31-35, North-Holland, Amsterdam, The Netherlands, 1987. · Zbl 0619.16024 [2] X.-K. Wang, “Derivations in prime near-rings,” Proceedings of the American Mathematical Society, vol. 121, no. 2, pp. 361-366, 1994. · Zbl 0811.16040 · doi:10.2307/2160409 [3] H. E. Bell and N.-U. Rehman, “Generalized derivations with commutativity and anti-commutativity conditions,” Mathematical Journal of Okayama University, vol. 49, no. 1, pp. 139-147, 2007. · Zbl 1139.16020 [4] Ö. Gölba\csi, “Notes on prime near-rings with generalized derivation,” Southeast Asian Bulletin of Mathematics, vol. 30, no. 1, pp. 49-54, 2006. · Zbl 1117.16033 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.