Remarks on derivations on semiprime rings. (English) Zbl 0746.16029

The main theorem of this short note proves that if \(R\) is a semi-prime ring with a nonzero ideal \(K\) and a derivation \(D\) which satisfies either \(D([x,y])=[x,y]\) for all \(x,y \in K\), or \(D([x,y])=-[x,y]\) for all \(x,y \in K\), then \(K\) is central.


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)
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