Hongan, Motoshi A note on semiprime rings with derivation. (English) Zbl 0879.16025 Int. J. Math. Math. Sci. 20, No. 2, 413-415 (1997). Let \(R\) denote a 2-torsion-free semiprime ring with center \(Z\), and \(I\) a nonzero ideal of \(R\). It is proved that \(I\subseteq Z\) if and only if \(R\) admits a derivation \(d\) having one of the following properties: (i) \(d([x,y])-[x,y]\in Z\) for all \(x,y\in I\); (ii) \(d([x,y])+[x,y]\in Z\) for all \(x,y\in I\); (iii) for each \(x,y\in I\), \(d([x,y])-[x,y]\in Z\) or \(d([x,y])+[x,y]\in Z\). This result generalizes earlier work of M. N. Daif and H. E. Bell [Int. J. Math. Math. Sci. 15, No. 1, 205-206 (1992; Zbl 0746.16029)]. Reviewer: H.E.Bell (St.Catherines) Cited in 25 Documents MSC: 16W25 Derivations, actions of Lie algebras 16N60 Prime and semiprime associative rings 16U70 Center, normalizer (invariant elements) (associative rings and algebras) 16U80 Generalizations of commutativity (associative rings and algebras) Keywords:central ideals; semiprime rings; center; derivations Citations:Zbl 0746.16029 PDFBibTeX XMLCite \textit{M. Hongan}, Int. J. Math. Math. Sci. 20, No. 2, 413--415 (1997; Zbl 0879.16025) Full Text: DOI EuDML